At the surface of unconventional superconductors so-called Andreev bound states may appear. These states carry currents which are directed opposite to the superconducting screening currents. We have studied various properties and consequences of these Andreev bound states. For example, we have studied, how these bound states influence the entry of a vortex into a superconductor [3,4]. In conventional superconductors the so-called Bean-Livingston barrier hinders the entrance of a vortex line due to the attractive force exerted by the mirror vortex from outside the surface. We found that in the presence of surface Andreev bound states the barrier is significantly increased, which means that the external magnetic field must be much (in the ideal case at low temperatures about 4-5 times) larger in order to drive the first vortex into the sample. This effect is more pronounced at low temperatures and possesses a characteristic angular dependence, which should allow an experimental confirmation of this effect. In different studies we found that surface Andreev bound states have a strong influence on the nonlinear Meissner effect at low temperatures [1] and they strongly influence the impurity scattering rates at the surface [2].