We discuss the semiclassical periodic orbit theory (POT) and some of its recent extensions which are applicable also to systems exhibiting a transition from integeable to chaotic behaviour. We apply the POT to give a semiclassical interpretation of shell effects in free metal clusters and semiconductor quantum dots in terms classical periodic orbits. In particular, we study the ground-state deformations of large metal clusters and discuss the recently observed conductance oscillations in a circular quantum dot under the influence of an external field. We also perdict the shell structure of a triangular quantum dot, using as models a triangular billiard and the Henon-Heiles potential including weak magnetic fields.