The Broyden-based input space mapping (SM) algorithm, better known as the aggressive space mapping (ASM) algorithm, is revisited in this article. The most fundamental SM-based optimization methods developed until now, in which ASM is framed, are overviewed. More than two decades of ASM evolution are briefly accounted, evidencing its popularity in both academia and industry. The two main characteristics that explain its popularity are emphasized: 1) simplicity, and 2) efficiency (when it works, it works extremely well). The fundamentals behind the Broyden-based input SM algorithm are illustrated, accentuating key steps for its successful implementation, as well as typical scenarios where it may fail. Finally, some future directions regarding ASM are ventured.