This article features one of the main trends in the development of neuroaesthetics and cognitive psychology of art, a systematic description of the mechanisms of aesthetic perception expressed in the creation of models. The paper analyzes six models of varying specification and capacity of extrapolating to other types of art. These are the following models: the neural network model, the neuropsychological model, the model of aesthetic perception of painting, the model of the intentions of the artist, the combined model of visual aesthetic experience, the model of aesthetic assessment and aesthetic judgments, and the Vienna integrated model of the processes of perception of art “top-down” and “bottom-up”. The possibilities and limitations of each model are considered according to such parameters as: the dynamics of aesthetic perception, the description of complex intermodal art forms, the extrapolation to different types of art, the measurement of aesthetic experience, the consideration of the interaction between the characteristics of the stimulus and the viewer, the detail of the esthetic experience description, the suitability for mathematical modeling. The most promising according to these criteria are the model of aesthetic assessment and aesthetic judgments, and the Vienna integrated model of the processes of perception of art “top-down” and “bottom-up”. In addition, the article provides an overview of existing approaches and research programs for modeling aesthetic experience. The paradigm of predictive processing (based on Bayesian inference) is considered as one of the most promising research programs. The key difficulties of modeling aesthetic experience are the lack of a unified research paradigm that includes a common understanding of the process of aesthetic perception and tools for its fixation, difficulties in formalizing and quantifying high-level components of aesthetic experience (expectations, schemes, experience, the viewer's “self”, etc.) and its continuity.