Summary: A review is given of model-based methods that have been used to solve ultrasonic nondestructive evaluation (NDE) flaw sizing problems. The focus of the review is on those challenging NDE flaw sizing problems where the flaw is small and the amount of scattering data that can be collected is limited. Various approaches for solving these inverse problems are described, with emphasis on methods based on the Born and Kirchhoff approximations. We discuss the sensitivity of these methods to noise, bandwidth limitations, and other issues that are important to the success or failure of these inverse approaches. As an alternative to these existing methods we discuss an approach based on the early-time flaw response. Finally, we describe some open issues that prevent a number of these methods from routinely being used in practice and describe some potential solutions.