Harmonic inversion is introduced as a powerful tool for semiclassical quantization, which solves the convergence problems in periodic orbit and closed orbit theory. The advantage of semiclassical quantization by harmonic inversion is the universality and wide applicability of the method to open and bound systems with underlying regular, chaotic, and even mixed classical dynamics. The method also allows the semiclassical calculation of diagonal matrix elements and, e.g. for atoms in external fields, individual non-diagonal transition strengths. We report recent improvements and extensions of the technique, e.g. semiclassical quantization with bifurcating orbits.