The recent discovery of topological states in condensed matter physics has spawned a quest for similar effects in classical physics. Topological insulators are bulk insulators supporting bandgap crossing, chiral edge states that are immune to backscattering caused by defects or disorder. Here, we present the acoustic equivalent of topological insulators, obtaining the analog of the Quantum Hall Effect (QHE) and the Quantum Spin-Hall Effect (QSHE) in acoustic metamaterials with, respectively, broken or preserved time-reversal sym- metry. We demonstrate how our recent results in the field of non-reciprocal acoustics [cf. Science 343 , 516 (2013); Ac. Today. 11 ,14 (2015)] can be used to induce an acoustic version of the QHE in active metamaterials with broken time-reversal symmetry. We also put forward resonant and non-resonant schemes to emulate the Kane-Mele Hamiltonian in completely passive acoustic metamaterials, obtaining the acoustic analog of the QSHE. Our work reveals that topological acoustic metamaterials enable fundamentally new ways of manipulating sound, including one-way, chiral propagation of acoustic waves over broad bandwidth and topological protection against geometry imperfections, impedance mismatches, crystal defects, and local disorder