This paper studies controllability and stabilizability of continuous piecewise affine dynamical systems which can be considered as a collection of ordinary finite-dimensional linear input/state/output systems, together with a partition of the product of the state space and input space into (full-dimensional) polyhedral regions. Each of these regions is associated with one particular linear system from the collection. The main results of the paper are Popov-Belevitch-Hautus-type necessary and sufficient conditions for both controllability and stabilizability of such systems.