I will discuss a particular limit of certain gauged linear sigma models called a Landau-Ginzburg point. Such points are computationally interesting as they may be used to compute, for example, the quantum cohomology (via mirror symmetry) of a toric hypersurface. I will present recent work (http://arxiv.org/abs/1004.2937) giving combinatorial conditions for the existence of such a point, and comment on some future directions.