  Recently, we witnessed a tremendous effort to conquer the realm of acoustics
as a possible playground to test with sound waves topologically protected wave
propagation. Acoustics differ substantially from photonic and electronic
systems since longitudinal sound waves lack intrinsic spin polarization and
breaking the time-reversal symmetry requires additional complexities that both
are essential in mimicking the quantum effects leading to topologically robust
sound propagation. In this article, we review the latest efforts to explore
with sound waves topological states of quantum matter in two- and
three-dimensional systems where we discuss how spin and valley degrees of
freedom appear as highly novel ingredients to tailor the flow of sound in the
form of one-way edge modes and defect-immune protected acoustic waves. Both
from a theoretical stand point and based on contemporary experimental
verifications, we summarize the latest advancements of the flourishing research
frontier on topological sound.
