Wafer fabs are built in various places around the world. But as you expect, the big fabs are located across Asia, more specially in Taiwan. This interactive map shows the location of major semiconductor foundries.
There are two types of business models for semiconductor foundry: a pure-play foundry and a non-pure-play foundry.
A non-pure-play foundry is a company that provides foundry services (wafer manufacturing) but in parallel they also produce and sell their own ICs.