I will survey the state of the art in the automated analysis of several classes of probabilistic infinite-state systems which naturally arise when studying probabilistic programs with recursive calls, queueing systems, population dynamics and natural language processing. I will describe the relationships between these different models and recent developments in the computational complexity of their analysis. I will also briefly describe tool PReMo, which is able to analyse these models, along with some interesting performance results. (This talk is based on several joint papers with T. Brazdil, V. Brozek, K. Etessami, S. Kiefer, A. Kucera, and M. Yannakakis).