Dynamical systems are often influenced by external signals. While periodically forced systems are well studied, much less is known about quasiperiodically forced systems, i.e. systems forced by two periodic signals with incommensurate frequencies. Strange non-chaotic attractors (SNA), a particular class of attractors, are typical for quasiperiodically forced systems. SNAs exhibit an intermediate behavior between regular (quasiperiodic) and chaotic motion. These attractors have a fractal-like structure in phase space, that is, in a geometrical sense they are strange . However, there is no sensitive dependence on initial conditions, which means they are non-chaotic in the dynamical sense. We develop a bifurcation theory for the appearance and disappearance of SNA via non-smooth bifurcations and study statistical properties of SNA.