Every ingredient (chemical) has a different function, and the combinations one could use them in are limitless. I'm not going to even pretend to be an expert at this.
Let's look at titanium dioxide, for starters. This is a chemical that is used in many different products, from paint to sunscreen. (By the way, don't be turned off by the word "chemical". As my fellow blogger Susan says, "...every single thing I touch, breathe, eat, hug, kiss, smell, taste, play, craft, and cuddle is made up of chemicals. The air I breathe (oxygen, nitrogen, and I'm sure a ton of farm soil as they till the fields around my house), the water I drink (hydrogen, oxygen, and a ton of fish pee!), the food I eat...and even my husband and adorable puppy are composed of various chemical compounds!")
What is titanium dioxide (TiO2)?
According to wikipedia, TiO2 "...is the naturally occurring oxide of titanium". It is commonly used as a pigment (it's SUPER white) and an opacifier in tons of household products: paint, toothpaste, sunscreen, plastic... even food (apparently it's used in skimmed milk to make it whiter. Weird!)
There are several reasons we use it in makeup. One is as a sunblock:
"Titanium dioxide is found in almost every sunscreen with a physical blocker because of its high refractive index, its strong UV light absorbing capabilities and its resistance to discolouration under ultraviolet light." (wikipedia)
It's similar to zinc oxide, which is another chemical commonly used in sunscreen (ya know, all those pictures of lifeguards on the beach with white noses? That's zinc oxide. I have never done that).
Also, it's incredibly white and opaque! It's used in a lot of foundations to vary how much coverage you get. A heavier coverage foundation will often have a lot of TiO2 in it. It also lightens colors dramatically.
It's truly a staple in any cosmetic manufacturer's supply closet. Keep your eyes open for other applications for it, because I promise it will surprise you!