This talk presents the basic framework for equilibrium pricing where agent heterogeneity is characterized by diverse beliefs. This turns out to be a tractable and sensible modelling framework in which to study various phenomena, which we will illustrate with several examples, drawn in the main from the literature on market selection. The Market Selection Hypothesis loosely speaking proposes that agents with `inferior' beliefs will eventually be `eliminated' from the market, but these terms need to be defined. Once they are, we are able to prove some results about when agents are indeed eliminated from the market; these results only partly confirm the intuition of the Market Selection Hypothesis. We have some surprising examples which show that some very unexpected phenomena may occur.