Inverse optimization has recently received a growing amount of attention as a data-driven approach to determining the values of modeling parameters for an optimization problem. The first part of this talk will introduce the concept of inverse optimization and present our contributions to recent advances in the theory of inverse optimization. We generalize the standard method of solving inverse optimization problems in situations that would otherwise lead to ill-posed inverse problems, and characterize the relationship between the generalized methods and the standard method in the literature. By building on the methods in a multiobjective optimization framework, we establish a new connection between inverse optimization and existing multiobjective optimization techniques. The second part of this talk will introduce radiation therapy treatment planning for cancer and illustrate how inverse optimization can be used to improve the treatment planning process. We propose a statistical model that predicts objective function weights from patient anatomy for prostate cancer radiation therapy treatment planning, leveraging the results of applying inverse optimization to historical treatments. This model provides a proof of concept for automated, geometry-driven weight determination.