The realistic simulation of complex deformable objects at interactive rates comprises a number of challenging problems, including deformable modeling, collision detection, and collision response. The deformable modeling approach has to provide interactive update rates, while guaranteeing a stable simulation. Furthermore, the approach has to represent objects with varying elasto-mechanical properties. The collision detection algorithm has to handle large numbers of geometrically complex objects. In particular, the algorithm has to detect self-collisions of deforming objects. The collision response method has to handle colliding and resting contacts among multiple deformable objects in a robust way. The method has to consider the fact that only sampled collision information is available due to the discretized object representations and the discrete-time simulation. The presentation discusses solutions to the aforementioned simulation aspects. Software demonstrations illustrate all models, algorithms, and their potential for applications such as surgery simulation.