Orthodontic biomechanics started in the early 1960s with the work of Burstone and later Nikolai. Experimental and theoretical studies using finite element methods (FEM) focused on the determination of the position of the center of resistance of single and multi-rooted teeth. Due to the complex structure of the system tooth/ periodontal ligament/ alveolar bone and because of the limited power of computers, the first numerical models were quite simple. Improved FE software, sophisticated programs for model generation and the explosion of computer power in the last decade resulted in more complex tooth-periodontium models and model assumptions. This paper describes the application of finite element methods in orthodontic biomechanics with the help of several typical examples. The examples cover aspects from basic orthodontic biomechanics to possible future applications in treatment planning using bone remodelling theories: determination of the mechanical properties of the periodontal ligament in a combined numerical and experimental study, calculation of the centers of resistance of different teeth, and simulation of orthodontic tooth movements. The examples show that nowadays finite element methods are a useful and easy-to-handle tool for the solution of a larger number of structure-mechanical and biomechanical problems. Nevertheless, in spite of the enormous technical progress in the last decade, many problems in orthodontic biomechanics remain to be solved. Keywords: orthodontics, biomechanics, finite element methods, center of resistance, bone remodelling theories, laser scanning, geometry reconstruction, surface matching