This paper is a survey of recent results on continuous-time Markov decision processes (MDPs) withunbounded transition rates, and reward rates that may beunbounded from above and from below. These results pertain to discounted and average reward optimality criteria, which are the most commonly used criteria, and also to more selective concepts, such as bias optimality and sensitive discount criteria. For concreteness, we consider only MDPs with a countable state space, but we indicate how the results can be extended to more general MDPs or to Markov games.