Inverse Optimization (IO) is based on the assumption that the observed process contains an implicit optimality criterion, and refers to inferring this criterion and the circumstances from data. We want to develop efficient numerical algorithms for (IO), driven by challenging applications. Standard MSO has matured to an efficient, stable, and versatile technology with hundreds of available software packages that foster the research of our time. In contrast, the solution of (IO) is currently based on few prototypical, application-specific, and inefficient numerical algorithms. Particular directions of research are development of numerically efficient strategies, based on all-at-once (multiple shooting) approaches, connections to Inverse Reinforcement Learning, implementation in a software package, specific treatment of integer control functions, optimum experimental design for (IO) problems, and application to mixed-urban-traffic optimization (autonomous and human drivers).