The two flavour enhancing sauces used extensively in Asian cooking would be Soy sauce and Fish Sauce.
Soy sauce originally had a contribution of fermented fish in its formulation. It's flavour is known as umami due to free glutamates and specific receptors on the tongue.

Soy sauce
Chinese name
Traditional Chinese
1. 醬油
2. 荳油
3. 豉油
Simplified Chinese
1. 酱油
2. 豆油
3. 豉油

Filipino name
Japanese name

Korean name

Thai name
ซีอิ๊ว (si-ew)

Vietnamese name
Quốc ngữ
xì dầu or nước tương

Soy sauce originated in China 2,500 years ago and its use later spread to East and Southeast Asia.  The recipe for Chinese soy sauce, 酱油 jiàngyóu, originally included fermented fish as well as soybeans.
Records of the Dutch East India Company list soy sauce as a commodity in 1737.
By the mid-19th century, the more expensive Japanese "shōyu" gradually disappeared from the European market and "soy sauce" became synonymous with the Chinese product.

Soy sauce may be made either by fermentation or by hydrolysis or Soy beans and possibly other grains such as wheat; some commercial sauces contain a mixture of fermented and chemical sauces.

Traditional soy sauces are made by mixing soybeans and grain with cultures such as Aspergillus oryzae and other related microorganisms and yeasts. Soy sauces were fermented naturally in giant urns and under the sun, which was believed to contribute additional flavors. Today some fermented sauces are made either traditionally or in factories.
Some soy sauces made in the Japanese way or styled after them contain about fifty percent wheat.

Acid-hydrolyzed vegetable protein
Some brands of soy sauce are often made from acid hydrolyzed soy protein instead of brewed with a traditional culture. This process may take only 3 days. Although they have a different flavor, aroma, and texture when compared to brewed soy sauces, they have a longer shelf-life and are more commonly produced for this reason. They are sometimes called Chemical Soy Sauce ("化學醬油" in Chinese) by those who prefer brewed sauces, but despite this name are widely used due to greater availability and lower prices. There is a clear delineation of preference for natural vs hydrolysed and advocates for each style. The clear plastic packets of dark sauce common with Chinese-style take out food typically use a hydrolyzed vegetable protein formula. Some higher-quality hydrolyzed vegetable protein products with no added salt, sugar or colorings are sold as low-sodium soy sauce alternatives called "liquid aminos" in health food stores, similar to the way salt substitutes are used.

Carcinogens have been identified in relatively recent times of Asian brands of Soy sauces. Some Vietnamese brands had levels of these up to 18,000 times maximal permissible levels. Some of these carcinogens may form during the manufacture of chemical sauce.Companies are obliged to remove these contaminants

Chinese soy sauce
Chinese soy sauce (simplified Chinese: 酱油; traditional Chinese: 醬油; pinyin: jiàngyóu; or 豉油 chǐyóu) is primarily made from soybeans, with relatively low amounts of other grains. There are two main varieties:
Light or fresh soy sauce (生抽 shēngchōu; or 酱清 "jiàng qing"; ): A thin (non-viscous), opaque, lighter brown soy sauce. It is the main soy sauce used for seasoning since it is saltier, less colourfully noticeable (due to its lighter colour), and also adds a distinct flavour. The light soy sauce made from the first pressing of the soybeans is called tóuchōu (simplified Chinese: 头抽; traditional Chinese: 頭抽), which can be loosely translated as first soy sauce or referred to as premium light soy sauce. Touchōu is sold at a premium because, like extra virgin olive oil, the flavor of the first pressing is considered superior. An additional classification of light soy sauce, shuānghuáng (雙璜), is double-fermented to add further complexity to the flavour. These last two more delicate types are used primarily for dipping.
Dark and old soy sauce (老抽 lǎochōu), a darker and slightly thicker soy sauce, is aged longer and contains added molasses to give it its distinctive appearance. This variety is mainly used during cooking since its flavour develops during heating. It has a richer, slightly sweeter, and less salty flavour than light soy sauce. Dark soy sauce is partly used to add color and flavour to a dish after cooking, but, as stated above, is more often used during the cooking process, rather than after.
In traditional Chinese cooking, these soy sauces were employed in strategic ways to achieve a flavour and colour for the dish.
Another type, thick soy sauce (醬油膏 jiàngyóugāo), is a dark soy sauce that has been thickened with starch and sugar. It is occasionally flavored with MSG. This sauce is not usually used directly in cooking but more often as a dipping sauce or poured on food as a flavorful addition.

Japanese soy sauce
Buddhist monks introduced soy sauce into Japan in the 7th centurywhere it is known as shoyu (醤油 shōyu?). The Japanese word tamari is derived from the verb tamaru (溜る?) that signifies "to accumulate", referring to the fact that tamari was traditionally a liquid byproduct produced during the fermentation of miso. Japan is the leading producer of tamari
Shōyu is traditionally divided into five main categories depending on differences in their ingredients and method of production. Most, but not all Japanese soy sauces include wheat as a primary ingredient, which tends to give them a slightly sweeter taste than their Chinese counterparts. They also tend towards an alcoholic sherry-like flavor, sometimes enhanced by the addition of small amounts of alcohol as a natural preservative. The widely varying flavors of these soy sauces are not always interchangeable, some recipes only call for one type or the other much like a white wine can't replace a red's flavor or beef stock does not produce the same results as fish stock.
Koikuchi (濃口?, "dark color"): Originating in the Kantō region, its usage eventually spread all over Japan. Over 80% of the Japanese domestic soy sauce production is of koikuchi, and can be considered the typical Japanese soy sauce. It is produced from roughly equal quantities of soybean and wheat. This variety is also calledkijōyu (生醤油) or namashōyu (生しょうゆ) when it is not pasteurized.
Usukuchi (淡口?, "light color"): Particularly popular in the Kansai region of Japan, it is both saltier and lighter in color than koikuchi. The lighter color arises from the usage of amazake, a sweet liquid made from fermented rice, that is used in its production.
Tamari (たまり?): Produced mainly in the Chūbu region of Japan, tamari is darker in appearance and richer in flavour than koikuchi. It contains little or no wheat; wheat-free tamari can be used by people with gluten intolerance. It is the "original" Japanese soy sauce, as its recipe is closest to the soy sauce originally introduced to Japan from China. Technically, this variety is known as miso-damari (味噌溜り), as this is the liquid that runs off miso as it matures.
Shiro (白?, "white"): A very light colored soy sauce. In contrast to tamari soy sauce, shiro soy sauce uses mostly wheat and very little soybean, lending it a light appearance and sweet taste. It is more commonly used in the Kansai region to highlight the appearances of food, for example sashimi.
Saishikomi (再仕込?, "twice-brewed") : This variety substitutes previously-made koikuchi for the brine normally used in the process. Consequently, it is much darker and more strongly flavored. This type is also known as kanro shōyu (甘露醤油) or "sweet shōyu".

Newer varieties of Japanese soy sauce include:
Gen'en (減塩?, "reduced salt"): Contains 50% less salt than regular shōyu for health conscious consumers.
Usujio (薄塩?, "light salt"): Contains 20% less salt than regular shōyu.
All of these varieties are sold in the marketplace in three different grades according to how they were produced:
Honjōzō (本醸造?, "genuine fermented"): Contains 100% genuine fermented product.
Kongō-jōzō (混合醸造?, "mixed fermented"): Contains genuine fermented shōyu mash mixed with 30–50% of chemical or enzymatic hydrolysate of plant protein.
Kongō (混合?, "mixed"): Contains Honjōzō or Kongō-jōzō shōyu mixed with 30–50% of chemical or enzymatic hydrolysate of plant protein.
All the varieties and grades may be sold according to three official levels of quality:[12]
Hyōjun (標準?): Standard grade. Contains more than 1.2% of total nitrogen.
Jyōkyū (上級 ?): Upper grade. Contains more than 1.35% of total nitrogen.
Tokkyū (特級?): Special grade. Contains more than 1.5% of total nitrogen.

Indonesian soy sauce
In Indonesia, soy sauce is known as kecap (also ketjap or kicap), which is a catch-all term for fermented sauces and may also be the source of the English word "ketchup". Five main varieties of Indonesian kecap exist:
Kecap asin
Salty soy sauce, which is very similar to Chinese light soy sauce, but usually somewhat thicker and has a stronger flavor; it can be replaced by light Chinese soy sauce in recipes.
Kecap manis
Sweet soy sauce, which has a thick, almost syrupy consistency and a pronounced sweet, treacle-like flavor due to generous addition of palm sugar. It is a unique variety; in a pinch, it may be replaced by molasses with a little vegetable stock stirred in.
Kecap manis sedang
Medium sweet soy sauce, which has a less thick consistency and a more saline taste than Manis.
Kecap inggris
("English fermented sauce"), or saus inggris ("English sauce") is the Indonesian name for Worcestershire sauce.
Kecap Ikan
is Indonesian fish sauce.

Malaysian soy sauce
In Singapore and Malaysia, soy sauce in general is dòuyóu (豆油); dark soy sauce is called jiàngyóu (醬油) and light soy sauce is jiàngqīng (醬清). Angmo daoiu (紅毛豆油, lit. "foreigners' soy sauce") is the Hokkien name for Worcestershire sauce.
Malaysia, which has language and cultural links with Indonesia, uses the word 'kicap' for soy sauce. Kicap is traditionally of two types: kicap lemak and kicap cair. Kicap lemak is similar to kecap manis but with very much less sugar while kicap cair is the Malaysian equivalent of kecap asin.

Korean soy sauce
Korean soy sauce, (called Joseon ganjang, 조선간장, in Korean) is a byproduct of the production of doenjang (Korean fermented soybean paste). They are mainly used in makingsoups, seasoning, and dip sauce. Joseon ganjang, thin and dark brown in color, is made entirely of soy and brine, and has a saltiness that varies according to the producer. Wide scale use of Joseon ganjang has been somewhat superseded by cheaper factory-made Japanese style soy sauce, called waeganjang (hangul: 왜간장/倭간장). According to the 2001 national food consumption survey in Korea, traditional fermented ganjang comprised only 1.4% of soy sauce purchases.[13]

Taiwanese soy sauce
The history of soy sauce making in Taiwan can be traced back to southeastern China, in the provinces of Fujian and Guangdong. Taiwanese soy sauce is perhaps most markedly known for its black bean variant, known as black bean soy sauce (黑豆蔭油). Most major soy sauce makers in Taiwan such as KimLan (金蘭), WanJaShan (萬家香), President-Kikkoman (統萬) make exclusive soybean and wheat soy sauce. A few other makers such as WuanChuang (丸莊), O'Long (黑龍), TaTung (大同) and RueiChun (瑞春) make black bean soy sauce, which takes longer to produce (about 6 months).
Vietnamese soy sauce
Vietnamese soy sauce is called xì dầu derived from Cantonese name 豉油, nước tương, or sometimes simply tương. It is used mostly as a seasoning or dipping sauce for a number of dishes. Vietnamese cuisine itself favors fish sauce in cooking but nước tương has a clear presence in vegetarian cooking.

Philippine soy sauce
A type of soy sauce based product which is a popular condiment in the Philippines is called toyo, usually found alongside other sauces such as fish sauce (patis) and sugar cane vinegar (suka). The flavor of Philippine soy sauce is a combination of ingredients made from soybeans, wheat, salt, and caramel, is interestingly milder compared to its Asian counterparts—possibly an adaptation to the demands of the Filipino palate and its cuisine. It is thinner in texture and has a saltier taste compared to its Southeast Asian counterparts, much more similar to the Japanese shōyu. It is used as a staple condiment to flavor many cooked dishes and as a marinade during cooking, it is also a table condiment, and is usually mixed and served with calamansi, a small Asian citrus-lime.

Further information: Soy allergy
Most varieties of soy sauce contain wheat, to which some people have a medical intolerance.  However, some naturally brewed soy sauces made with wheat may be tolerated by people with a specific intolerance to gluten because gluten is not detectable in the finished product. Japanese tamari soy sauce is traditionally wheat-free, and some tamari available commercially today is wheat- and gluten-free.

A 2001 test of various soy sauces and related products by the United Kingdom Food Standards Agency (FSA) found that 22 out of 100 samples contained a substance called3-MCPD (3-monochloropropane-1,2-diol) at levels considerably higher than those deemed safe by the European Union. About two-thirds of the 22 samples also contained a second chemical called 1,3-DCP (1,3-dichloropropane-2-ol) which experts advise should not be present at any levels in foodBoth chemicals are carcinogenic(have the potential to cause cancer), and 1,3-DCP can cause genetic damage to be passed on to offspring who never consumed the sauces. The FSA recommended that the affected products be withdrawn, and in June 2001 issued a Public Health Advice leaflet warning against a small number of soy sauce products that were found to contain high levels of potentially cancer-causing chemicals. The leaflet singled out brands and products (some by batch numbers) imported from Thailand, China, Hong Kong and Taiwan. Although the leaflet primarily looked at soy sauce, it also included oyster sauce, marinades and other types of sauces, that affected the brands Golden Mountain,King Imperial, Pearl River Bridge, Jammy Chai, Lee Kum Kee, Golden Mark, Kimlan, Golden Swan, Sinsin and Tung Chun. Despite these being small in number in the UK, they are the dominant brands in their respective nations.
In Vietnam 3-MCPD was found in toxic levels (In 2004 the HCM City Institute of Hygiene and Public Health found 33 of 41 sample of soya sauce with high rates of 3-MCPD, including six samples with 11,000 to 18,000 times more 3-MPCD than permitted, compared to about 5,000 times in 2001) in soy sauces there in 2007, along with formaldehyde in the national dish Pho, and banned pesticides in vegetables and fruits.