In the past decades mathematical optimization has found its way into radiation therapy and has made profound practice changing impact. Today, virtually all advanced treatment delivery methods, such as IMRT, VMAT, tomotherapy, LDR/HDR brachytherapy, proton therapy, are based on some form of optimization approach that changes the treatment variables (beam intensities, multileaf collimator shapes, beam angles, dwell times and seed or source positions) in the planning computer using an optimization algorithm, until the best value of the treatment (planning) objective has been found. It is fair to say though that a truly optimal radiation treatment plan remains elusive. The reasons for that include difficulties in defining meaningful planning objectives and constraints in mathematical terms, various uncertainties in the planning and delivery process, and the inability of optimization algorithms to find the true optimum. Radiation therapy optimization therefore remains an active field of research.