In the last 40 years, low energy electron diffraction (LEED) has proved to be the most reliable quantitative technique for surface structural determination. In this review, recent developments related to the theory that gives support to LEED structural determination are discussed under a critical analysis of the main theoretical approximation-the muffin-tin calculation. The search methodologies aimed at identifying the best matches between theoretical and experimental intensity versus voltage curves are also considered, with the most recent procedures being reviewed in detail.