This article presents an overview of modern scientific research on budget risks as a factor influencing the sustainable development of territories. Certain aspects of the budget risk category were clarified based on an analysis of the existing conceptual framework of budget risk theory. The main types of budget risks are highlighted and the relationship between them is reflected. The main risk factors of the municipal budget corresponding to each type of risk were also identified. Also, recommendations on the methodology for assessing budget risks are provided. They are based on the use of correlation and regression analysis methods, as well as the simulation modeling of budget risk indicators. This methodological approach will allow for scenario analysis, stress testing of key budget indicators, and improvement of the quality of financial management. This will increase the resilience of budgets to the impact of uncertainty and risk factors.