Aqueous Mg batteries are promising energy storage and conversion systems to cope with the increasing demand for green, renewable and sustainable energy. Realization of high energy density and long endurance system is significant for fully delivering the huge potential of aqueous Mg batteries, which has drawn increasing attention and investigations. ••Recent advances in anode and electrolyte for aqueous Mg batteries are reviewed.••An in-depth understanding of Mg anode self-discharge is given.••Application of computational methods assisted by machine learning is discussed.Aqueous Mg batteriesAnodeElectrolyteMachine learningThe world has witnessed the increasing demand for non-fossil fuel power sources with large capacity, high power, low cost and reliable safety. This has put pressure on commercially available energy technologies like lithium-ion batteries and, therefore, leads to the search for better alternatives involving researchers worldwide in the past decades. Fig. 1 summarizes the key features of relevant metals as candidates for energy storage as battery anode,,,, among which metallic Mg has been regarded as a rising star owing to its well-balanced comprehensive properties like highly negative redox potential (–2.37 VSHE), favourable volumetric capacity (3832 mA h cm–3), low materials cost and great chemical stability. Mg metal can act as anode for both secondary batteries (electrochemically rechargeable) and primary batteries (electrochemically non-rechargeable) combined with proper electrolytes and cathode materials. Secondary Mg batteries have experienced remarkable development since the first time successful construction of a working Mg-ion battery prototype in 2000 but are still beyond industrial interests of commercialization. Proper combinations of anode/electrolyte/cathode enabling high voltage/high capacity batteries are still under research. Secondary Mg-ion batteries normally use ether-based organic electrolytes to ensure reversible plating/stripping of pure Mg anodes [6,7]. These ethereal electrolytes however are mostly corrosive and sensitive to air and humidity, resulting in safety hazar. Self-discharge of batteries is normally referred to chemical or electrochemical processes causing a net capacity loss of the battery system. Concerning aqueous Mg batteries, there are three processes from anode side that could result in capacity loss, namely (i) corrosion, (ii) self-corrosion and (iii) chunk effect as shown in Fig. 3. Corrosion refers to the dissolution of Mg anodes at open circuit condition (OCP, i.e. non-discharge interval), which normally involves hydrogen evolution reaction (HER) and oxygen reduction reaction (ORR) [26,27]. By comparison, self-corrosion means the wasteful dissolution of Mg anodes during discharge (with applied current). Different to the electrons released by Mg anodic dissolution for current generation, electrons released by self-corrosion are mainly consumed via water reduction leading to fast hydrogen evolution on the anode surface, which in turn causes the need for gas venting for aqueous Mg batteries. Mg anodes self-corrosion is associated with the well-known NDE (negative difference effect, recently termed as anomalous hydrogen evolution) on Mg and its alloys under polarization with the mechanism remaining controversial,,. Chunk effect refers to the separation of undissolved anode particles from Mg substrate leading to separated chunks, which cannot be used for current generation but simply corrode as stand-alone micro-particles. The occurrence of chunk effect is basically related to inhomogeneous dissolution of the anode during discharge as shown in Fig. 4 (.