The paper deals with the realization theory of linear switched systems. Necessary and sufficient conditions are formulated for a family of input–output maps to be realizable by linear switched systems. Characterization of minimal realizations is presented. The paper treats two types of linear switched systems. The first one is when all switching sequences are allowed. The second one is when only a subset of switching sequences is admissible, but within this restricted set the switching times are arbitrary. The paper uses the theory of formal power series to derive the results on realization theory.