Foodstuffs are in many instances concentrated suspensions that exhibit a very complex rheological behavior. In this chapter, we review basic concepts on the rheology of suspensions. Problems and difficulties encountered in rheometry are discussed. Examples of the complex behavior of model suspensions and of a few foodstuffs are presented. The rheological properties of peanut butter are typical of many food products and our recent results are used to illustrate rheological complexity. In particular, we discuss wall slip effects, yield stress measurement, thixotropic behavior, strain-induced hardening, and nonlinear effects.