The article addresses matters concerned with digitalization and intellectualization of district heating systems (DHS) and is of a reviewing and problem-stating nature. Intellectualization of DHSs is viewed as a process of transition for a fundamentally new platform, within which it becomes possible to efficiently coordinate the interests, requirements, and capacities of all stakeholders participating in the heat-supply processes, and the consumer is given the role of an active full-fledged participant. The main lines, aims, and features of this process are briefly characterized. Both domestic and foreign experience gained from setting up centralized (district) heat-supply systems, including the most advanced development trends of these systems in EU member states. Special attention is paid to matters concerned with intellectualization of Russian DHSs. It is shown that the transition for a new paradigm will generate the need to cardinally revise the existing practices of DHS design, operation, and supervisory (dispatch) control. The key lines and tasks connected with transition to the new concept of managing the operation of DHSs as cyberphysical objects are formulated. The transition to this concept implies a wide use of mathematical and computer modeling methods for automating the DHS state monitoring processes, its analysis, prediction, and optimization. A significant part of the article is devoted to an analytical review of the current state of scientific-methodical developments in this field in four basic lines: mathematical modeling of DHS operation modes (hydraulic, temperature and thermal-hydraulic, stationary and dynamic, deterministic and probabilistic), identification of the DHS's actual state (equipment characteristics, operating parameters, etc.) based on measurement data, optimization of DHS operation modes (for estimating the effectiveness of new heat-supply technologies, efficient DHS operation, and optimal control of DHS operation modes), and software for computer modeling of DHSs. Informative statements of DHS mathematical and computer modeling tasks are described along with the background developments for solving them available at ESI SB (Russian Academy of Sciences) are described.