Within the set of risk factors that compromise the conservation of marine biodiversity, one of the least understood concerns is the noise produced by human operations at sea and from land. Many aspects of how noise and other forms of energy may impact the natural balance of the oceans are still unstudied. Substantial attention has been devoted in the last decades to determine the sensitivity to noise of marine mammals—especially cetaceans and pinnipeds— and fish because they are known to possess hearing organs. Recent studies have revealed that a wide diversity of invertebrates are also sensitive to sounds, especially via sensory organs whose original function is to allow maintaining equilibrium in the water column and to sense gravity. Marine invertebrates not only represent the largest proportion of marine biomass and are indicators of ocean health but many species also have important socio-economic values. This review presents the current scientific knowledge on invertebrate bioacoustics (sound production, reception, sensitivity), as well as on how marine invertebrates are affected by anthropogenic noises. It also critically revisits the literature to identify gaps that will frame future research investigating the tolerance to noise of marine ecosystems.