Thermal-mechanical processing by laser radiation has been shown effective in forming plates into relatively complex shapes at economically supportable rates. While simulation models to predict deformation given a set of process parameters exist and continue to be improved, few attempts have been made to solve the so-called inverse problem. This inverse problem can be defined as determining the locations and processing parameters of the heating paths that will result in a desired deformation. The calculation of these heating paths is an under-constrained problem with essentially infinite potential solutions. Recent research efforts at several international institutions have provided various strategies for solving this problem. This paper discusses these strategies, as well as the most recent developments from the ongoing efforts at the Applied Research Laboratory and at the Department of Mechanical Engineering, both of Penn State University.