Magnesium (Mg) metal has been widely explored as an anode material for Mg-ion batteries (MIBs) owing to its large specific capacity and dendrite-free operation. However critical challenges, such as the formation of passivation layers during battery operation and anode-electrolyte-cathode incompatibilities, limit the practical application of Mg-metal anodes for MIBs. Motivated by the promise of group XIV elements (namely Si, Ge and Sn) as anodes for lithium-and sodium-ion batteries, here we conduct systematic first principles calculations to explore the thermodynamics and kinetics of group XIV anodes for Mg-ion batteries, and to identify the atomistic mechanisms of the electrochemical insertion reactions of Mg ions. We confirm the formation of amorphous MgxX phases (where X = Si, Ge, Sn) in anodes via the breaking of the stronger X-X bonding network replaced by weaker Mg-X bonding. Mg ions have higher diffusivities in Ge and Sn anodes than in Si, resulting from weaker Ge-Ge and Sn-Sn bonding networks. In addition, we identify thermodynamic instabilities of MgxX that require a small overpotential to avoid aggregation (plating) of Mg at anode/electrolyte interfaces. Such comprehensive first principles calculations demonstrate that amorphous Ge and crystalline Sn can be potentially effective anodes for practical applications in Mg-ion batteries.Consequently, the active search for alternative anode materials, in particular, insertion-type anodes for MIB, is necessary.Relative to Li-and Na-ion batteries, much less is known about suitable insertion-type anodes and the associated electrochemical reactions for MIBs due to the unique challenge of identifying host materials with appropriate electrochemical capacities that allow for repeated cyclic insertion and deinsertion. Although the ionic radius of Mg (0.72 Å) is smaller than that of Li and Na (0.76 Å X=Si, Ge, Sn, respectively (see S2 in Supporting Information). After correcting the diffusivities for the inherent stresses at different temperatures, Arrhenius relation 53D D E k T was used to extrapolate the diffusivities at 300 K, Eba, kB, T, D0 being the energy barrier, the Boltzmann constant, temperature and the prefactor. Figure 4 shows the intrinsic diffusivities of Mg and X atoms at 300 K for different values of coupling parameters for all anodes considered here. The magnitudes of the residual compressive stresses are listed in energy barriers of Mg and X species in crystalline and amorphous X anodes; supporting table exhibiting the average inner stress induced by magnesiation in Mg-X systems (PDF).