With the rapid development of transcatheter heart valve replacement and repair, heart valve modeling and simulation have been increasingly applied in heart valve product development, risk assessment, and surgical planning, playing an increasingly important role. At the same time, with the rapid advancement of artificial intelligence in the field of modeling and simulation, heart valve modeling and simulation also show some new development directions and trends, especially rapid modeling and simulation, which make preoperative planning based on modeling and simulation possible. This paper summarizes and analyzes the relevant progress of heart valve modeling and simulation over the past decade, covering the four heart valves— aortic, pulmonary, mitral, and tricuspid—as well as various devices for valve diseases, including geometric modeling methods, mathematical and physical modeling methods, numerical simulation algorithms, and clinical applications. At the same time, it systematically summarizes and forecasts the engineering problems and challenges in heart valve modeling and simulation, as well as its applications in device development and clinical surgical planning.