One of the most fundamental properties of any class of dynamical systems is the study of well-posedness, i.e. the existence and uniqueness of a particular type of solution trajectories given an initial state. In case of interaction between continuous dynamics and discrete transitions this issue becomes highly non-trivial. In this survey an overview is given of the well-posedness results for complementarity systems, which form a class of hybrid systems described by the interconnection of differential equations and a specific combination of inequalities and Boolean expressions as appearing in the linear complementarity problem of mathematical programming.