Magnesium-based batteries represent one of the successfully emerging electrochemical energy storage chemistries, mainly due to the high theoretical volumetric capacity of metallic magnesium (i.e., 3833 mAh cm−3 vs. 2046 mAh cm−3 for lithium), its low reduction potential (−2.37 V vs. SHE), abundance in the Earth’s crust (104 times higher than that of lithium) and dendrite-free behaviour when used as an anode during cycling. However, Mg deposition and dissolution processes in polar organic electrolytes lead to the formation of a passivation film bearing an insulating effect towards Mg2+ ions. Several strategies to overcome this drawback have been recently proposed, keeping as a main goal that of reducing the formation of such passivation layers and improving the magnesium-related kinetics. This manuscript offers a literature analysis on this topic, starting with a rapid overview on magnesium batteries as a feasible strategy for storing electricity coming from renewables, and then addressing the most relevant outcomes in the field of anodic materials (i.e., metallic magnesium, bismuth-, titanium- and tin-based electrodes, biphasic alloys, nanostructured metal oxides, boron clusters, graphene-based electrodes, etc.).