In this paper using results taken directly from linear matrix algebra we shall present a survey of the new results on controllability for linear both continuous-time and discrete-time switched dynamical systems with unconstrained admissible controls. Controllability problems for different types of dynamical systems require the application of numerous mathematical concepts and methods taken directly from differential geometry, functional analysis, topology, matrix analysis and theory of ordinary and partial differential equations and theory of difference equations. In the paper we will use mainly statespace models of dynamical systems, which provide a robust and universal method for studying controllability of various classes of systems.