The migration of various cell populations partially relies on chemotaxis meaning that cells direct their movement in response to the gradient of a chemical signal. Widely used macroscopic models for chemotaxis are Keller-Segel systems consisting of partial differential equations. As one feature they can describe the spontaneous formation of cell aggregation. One analytical challenge related to that feature is the detection of unbounded solutions, the so-called blow-up. We will present several blow-up results for Keller-Segel systems and outline the main stategies of their proofs.