In the article, based on the analysis of available sources of information, information on various types of modeling is systematized and presented, an improved classification is proposed according to which one can distinguish: full, incomplete and approximate (in completeness); stochastic and deterministic (by degree of certainty); discrete, discrete-continuous, continuous (by intermittence); static and dynamic (by the change in time); constructive and descriptive (by the presence of controlled variables); functional, information, behavioral (depending on the aspect of modeling); educational, experimental, scientific and technical, game and imitation (in the field of modeling); mental and real (in the form of implementation); the real, depending on the method of implementation, is divided into the natural (scientific experiment, complex tests, production experiment) and physical (in real time, model time and without time); depending on whether the computer is used for mental modeling is divided into computer and non-computer. By the way of realization, the mental is divided into visual (hypothetical, analog and mocked), symbolic (linguistic and sign) and mathematical (situational, cybernetic, structural, analytical, algorithmic and combined). Also, the mathematical, depending on the properties reflected, is divided into geometric, probabilistic and topological. The article presents historical facts related to the stages of the development of modeling. Causes and main directions of development of modeling and direction of human activity are indicated, in which modeling currently performs one of the main roles.