The two main approaches for modeling mechanical systems with unilateral contacts and friction are the regularized and the non-smooth approach. In the following, the two approaches are introduced using a simple example. Consider a block which can slide or stick on a table (see figure 1a). The motion of the block is described by the equation of motion, whereas the friction force is unknown (see figure 1b). In order to obtain the friction force, a separate force law must be specified which links the friction force to the associated velocity of the block.