The postproduction test of integrated circuits is crucial to ensure a high quality of the final product. This test is carried out by checking the correct response of the chip under predefined input stimuli – or test patterns. These patterns are calculated by algorithms for Automatic Test Pattern Generation (ATPG). The basic concepts and algorithms for ATPG are reviewed in this chapter. Then, an advanced SAT-based ATPG tool is introduced and emprically evaluated.