Abstract This article presents mainly a review of the modern state of the theory of glasses as compared to the principal experimental data, which are briefly surveyed. Some basic experimental data and phenomenological approaches in glass physics are considered in the introduction (chapter 1). The first part of the review contains a consideration of models of the structure and topology of glasses (chapter 2) and of the glass transition (chapter 3). The nature of important long-time relaxation processes in glass-forming liquids and glasses is briefly discussed (chapter 4 and partly chapter 6). The second part of the survey deals with fundamental properties of glasses which are commonly referred to as anomalous in the sense that they are not characteristic of crystals. Two correlated sets of anomalous properties are considered: universal low-temperature properties of glasses (chapters 5 and 6) and electron properties of glassy semiconductors (chapters 7 and 8). Attention is focused on fundamental concepts, models, results and problems of the theory. A summary and some actual problems of the theory are presented in chapter 9. The review contains a discussion of theoretical results and experimental data which had come to the author's attention mainly up to the beginning of 1987.