The Lie-Trotter formula for strongly continuous semigroups of operators in Banach spaces provides conditions such that switching between two deterministic systems (represented by two of those semigroups) results into new combined dynamics (i.e. a new semigroup) in the limit of infinitely fast switching. We discuss the history of the formula and exhibit then recently obtained results that apply to switching of Markov semigroups, which correspond to Markov processes in continuous time.