Many sophisticated distributed real-time systems and modeling languages can be formalized in rewriting logic as real-time rewrite theories, which can be analyzed using the Maude and Real-Time Maude tools. In this paper we show how real-time rewrite theories, possibly with user-defined timed strategies, can be specified and analyzed directly in Maude, using both explicit-state and symbolic executions. We then give an overview of applications of Maude and Real-Time Maude to real-time and cyber-physical systems and modeling languages, showing that such analysis can provide useful insights about advanced systems that cannot be easily (or at all) formalized using decidable formalisms such as timed automata. This work also shows the predictive power of model-based performance estimation using statistical model checking.