The goal of clean renewable energy production has promoted the large-scale deployment of marine renewable energy devices, and their associated submarine cable network. Power cables produce both electric and magnetic fields that raise environmental concerns as many marine organisms have magneto and electroreception abilities used for vital purposes. Magnetic and electric fields' intensities decrease with distance away from the cable. Accordingly, the benthic and the sedimentary compartments are exposed to the highest field values. Although marine invertebrate species are the major fauna of these potentially exposed areas, they have so far received little attention. We provide extensive background knowledge on natural and anthropogenic marine sources of magnetic and electric fields. We then compile evidence for magneto- and electro-sensitivity in marine invertebrates and further highlight what is currently known about their interactions with artificial sources of magnetic and electric fields. Finally we discuss the main gaps and future challenges that require further investigation.