In this talk, we review several results regarding the stability analysis of linear systems of fractional differential equations. Starting from the well-known results of Matignon on the stability of single-order systems, the presentation is geared towards multi-order systems, as well as linear multi-term fractional differential equations with Caputo derivatives. Discrete-time counterparts of the obtained results are also presented, in the framework of systems of fractional-order difference equations with Caputo-type differences.