With the steady advancement of major national engineering projects, the construction scale of long deeply buried tunnels and deep rock mass projects has been expanding year by year. Engineering hazards frequently occur, including large surrounding rock deformation, rock bursts and collapses induced by high geostress, which severely threaten construction safety and long-term operational stability. The formation and evolution of geostress are jointly governed by deep earth dynamics, intrinsic rock mass properties and external environmental factors. Acquiring accurate geostress data is of great significance for the construction of deep rock mass projects. This paper firstly systematically sorts out five major dynamic formation mechanisms of geostress, and analyzes the control laws of geological structures, landforms, rock mechanical properties and other factors on the spatial distribution of geostress. On this basis, mainstream geostress measurement techniques, namely hydraulic fracturing, borehole wall deformation, borehole bottom stress relief, stress recovery and acoustic emission method are classified and elaborated. The measuring principles, operational procedures, applicable conditions, advantages and limitations are discussed. Furthermore, commonly adopted geostress calculation approaches are summarized from three dimensions: theoretical analysis, numerical simulation and intelligent algorithms. The fundamental principles and application characteristics of classical elastic mechanics algorithms, numerical simulation methods and intelligent algorithms are illustrated in detail, and the factors affecting the calculation accuracy of different methods are investigated. Finally, suggestions are put forward in terms of upgrading testing equipment, improving multi-field coupled geostress calculation models, and realizing deep integration between intelligent algorithms and traditional methods. The presented research can provide valuable references for engineering investigation, deep rock drilling, mining and related engineering practices.