In this talk, I will discuss why topology, a branch of mathematics not often covered in the curricula of acousticians, can nevertheless play an important role in the control of acoustic resonances and scattering. After an introductory crash course on homotopy, I will provide a few simple examples where natural acoustic properties can be better understood through the lens of topology. I will then explain how it is possible to engineer the topology of acoustic systems, leveraging architected topological materials to turn an otherwise sensitive acoustic effect, such as transmission poles or zeros, into something robust and topologically-protected. Experiments and potential applications will be discussed, before concluding on extensions to 2D systems.