High precision positionning and assembly as well as micro-machining require dedicated devices. These devices have to provide high repeatability and precision on several degrees of freedom (dof). High dynamic characteristics are also sought to reach short task execution time and a good robustness. This work shows how to design parallel robots with flexure joints that allow nanometric positionning repeatability and high dynamics. After a description of the state of the art, a design methodology is proposed. The state of the art is focused on several topics (analyses and design of flexure joints, parallel micro-robots, dynamic and control of high precision dynamic devices). The methodology guides the engineer through the different design-steps. The design of elementary flexures is studied and the concept of functionaly equivalent flexures is given. This concept consists in a comparison criterion for elementary flexures. The idea is to compare elements that allow a given displacement (for instance a bending angle) at maximal stress. The caracteristics of flexure joints are described. Stiffness and compliance matrix, accurary, eigen-frequencies and eigen-modes determine the behaviour of a joint. The flexure profile, mass-geometry and material choices are analysed. The links between a structure, its dynamic model and the controller are investigated. Several examples are proposed to assess the effect of the mechanical properties of the chosen structures. Two devices have been built to emphasize important issues encountered in the design and control of high precision flexure robots. The first one is a linear stage that highlights the importance of identification, sensitivities, algorithms, quantifications (control and mesure) and sampling on a single dof structure. The second one is a 3 dof parallel robot used as a micro electro-discharge machine. The properties and caracteristics of this robot are illustrated. Some questions like the calibration or the choice of the kinematics are still open.