In this paper, we overview recent advances in high-precision structure calculations of the hydrogen molecular ions ( and HD+), including nonrelativistic energy eigenvalues and relativistic and quantum electrodynamic corrections. In combination with high-precision measurements, it is feasible to precisely determine a molecular-based value of the proton-to-electron mass ratio. An experimental scheme is presented for measuring the rovibrational transition frequency (v,L) : (0,0) → (6,1) in HD+, which is currently underway at the Wuhan Institute of Physics and Mathematics.