The Markov-additive process family represents a natural theoretical framework to study the so-called regime-switching models. Models with regime-switching features find applications in finance and insurance insofar as they provide a mathematical description for a price process that evolves against a macro-economic canvas determining parameters changing over regimes. Stock or insurance dynamics can be described that take into account the backdrop economical scenario (crisis vs stability for instance). Theoretical as well as ad-hoc applications in collective risk theory and finance are explored under this research program. This has produced some research articles on fluctuation theory, ruin theory as well as estimation methodology.