Although much remains unknown about the dark matter of the universe, one property is normally considered sacrosanct: dark matter must be stable well beyond cosmological time scales. However, a new framework for dark-matter physics has recently been proposed which challenges this assumption. In the «dynamical dark matter» (DDM) framework, the dark sector consists of a vast ensemble of individual dark-matter components with differing masses, lifetimes, and cosmological abundances. Moreover, the usual requirement of stability is replaced by a delicate balancing between lifetimes and cosmological abundances across the ensemble as a whole. As a result, it is possible for the DDM ensemble to remain consistent with all experimental and observational bounds on dark matter while nevertheless giving rise to collective behaviors which transcend those normally associated with traditional dark-matter candidates. These include a new, non-trivial darkmatter equation of state as well as potentially distinctive signatures in collider and direct-detection experiments. In this review article, we provide a self-contained introduction to the DDM framework and summarize some of the work which has recently been done in this area. We also present an explicit model within the DDM framework, and outline a number of ideas for future investigation.