Not just mayonnaise: fat and water based compounds are used in many different types of sauce. Here are the main ones:
This is probably the simplest one to prepare. Made with four parts oil to one part lemon, and a pinch of salt, it is ideal to dress grilled or boiled fish, as well as vegetables and salads. It is an "unstable" emulsion, meaning it tends to separate.
There are many variants on the classic recipe, generally obtained by substituting the mustard with other ingredients. With a few crushed cloves of garlic you get Aioli, with garlic and green and red peppercorns, Andalusian sauce, and with a few spoons of whipped cream, Chantilly mayonnaise.
One of the best-known white sauces, excellent with carpaccio and delicate fish dishes. The recipe uses three egg yolks, 175 grams of clarified butter, the juice of half a lemon, salt and pepper. This sauce is prepared hot, which helps it to emulsify. Béarnaise sauce is another variant, made by first preparing a base of red wine vinegar, boiled with pepper, tarragon and shallots; it is perfect with broiled meats.
Vinaigrette is very similar to Citronette, except for one ingredient: instead of lemon, it uses white wine vinegar. In order to make the emulsion stable, so that it won't separate, some cooks add a teaspoon of mustard, which acts as an emulsifier.