This survey aims at providing a comprehensive overview of the recent trends in the field of modeling and simulation (M&S) of interactions between users and recommender systems and applications of the M&S to the performance improvement of industrial recommender engines. We start with the motivation behind the development of frameworks implementing the simulations -- simulators -- and the usage of them for training and testing recommender systems of different types (including Reinforcement Learning ones). Furthermore, we provide a new consistent classification of existing simulators based on their functionality, approbation, and industrial effectiveness and moreover make a summary of the simulators found in the research literature. Besides other things, we discuss the building blocks of simulators: methods for synthetic data (user, item, user-item responses) generation, methods for what-if experimental analysis, methods and datasets used for simulation quality evaluation (including the methods that monitor and/or close possible simulation-to-reality gaps), and methods for summarization of experimental simulation results. Finally, this survey considers emerging topics and open problems in the field.