It is well-known that in principle automatic test pattern generation (ATPG) can be solved by transforming the circuit and the fault considered into a Boolean satisfiability (SAT) instance and then calling a so-called SAT solver to compute a test. More recently, the potential of SAT-based ATPG has been significantly extended. In this paper, we first provide introductory knowledge on SAT-based ATPG and then report on latest developments enabling applications far beyond classical ATPG.