We've already mentioned that pectic enzymes can help to clear up the haze in your wine, but they only work on the residue that fruit pectins leave behind. Several other clarifiers and fining agents are used to clean up yeast and other stray particles by helping sediments drop out of the wine so that they can be easily strained out or simply left at the bottom of the barrel (or bottle).
And while the job of clarifiers is to, well, clarify, you'd never guess it by hearing what they're made of. One common fining agent, called bentonite, is a fine clay made from volcanic ash that works by attracting positively charged particles. Others, such as Sparkolloid (made from fossilized algae) or chitosan (made from the exoskeletons of crustaceans) are positively charged, meaning that they attract and help to isolate negatively charged sediments. No one fining agent can clean up your wine on its own; instead, they work with one another (and with other wine components) to get the job done.