Inverse approaches and, in particular, intensity modulated radiotherapy (IMRT), in combination with the development of new technologies such as multi-leaf collimators (MLCs), have enabled new potentialities of radiotherapy for cancer treatment. The main mathematical tool needed in this connection is numerical optimization. In this article, the variety of continuous optimization approaches, which have been proposed for the computation of optimal beam and beamlet intensities respectively, is surveyed and discussed. The discussion includes a nonlinear optimization model for IMRT with biologically motivated goals, which has recently been presented by the authors and is accompanied by a sensitivity analysis proposed by Alber et al.. At last, new developments in intensity modulated proton therapy (IMPT) are considered. It is shown by a clinical case example that the algorithm introduced by the authors earlier is also capable to solve, within a few minutes of computation times, the much larger problems of treatment planning for the IMPT spot-scanning technique.