Resources used in Li-ion batteries are becoming more expensive due to high demand, and the global cobalt market heavily depends on supplies from countries with high geopolitical risks. Alternative battery technologies including Mg-ion batteries are therefore desirable. While the formation of Mg dendrites on metal Mg anodes in magnesium-ion batteries is still very controversial, alloy anodes have been proposed to replace the metal anodes and avoid the dendrites formation. Conventional solid alloy anodes suffer from significant volume changes (up to 300%) during cycling, leading to poor cycling performance. To address this issue, "self-healing" anodes have emerged as a promising approach. These anodes consist of liquid metals or liquid alloys that undergo reversible liquid-solid phase transformations during charging and discharging cycles, recovering themselves from any deformation-induced material failure. This dissertation presents several key findings. Firstly, we demonstrate the growth of Mg dendrites in hybrid Mg(TFSI)2/aluminum chloride/magnesium chloride in 1, 2-dimethoxyethane electrolyte during electrodeposition at various current densities using a symmetric cell. Secondly, we show the liquid-solid phase transformations in liquid metals and alloys (Ga, GaIn), which can be used as “self-healing” Mg-ion battery anodes to overcome the failure of degradation in solid Mg-ion batteries anode. The storage mechanism and morphology evolution during self-healing is also studied. Finally, we investigate the significant volume and shape changes in solid anodes of Li-ion batteries. Overall, this dissertation provides valuable insights into self-healing liquid electrodes in Mg-ion batteries and shape change metal electrodes in Li-ion batteries.