Two-dimensional correlated electronic systems presenta fundamental challenge in condensed matter and quantum physics.Thermal tensor networks have emerged as apowerful tool for finite-temperature studies ofthe many-electron systems. In this talk, I will present ourrecent advances in thermal tensor networkmethods, focusing on two recentdevelopments: (1) exponential tensor renormalization group(XTRG), which achieves exponential acceleration through densitymatrix operator squaring, and (2) the efficienttangent-space tensor renormalization group (tanTRG) that incorporatestime-dependent variational principle (TDVP) techniques. Our tensornetwork methods enable accurate simulationsof fundamental models like the Hubbard and t-J Hamiltonians, as wellas material-specific applications such as the t-t’-J model forcuprates and the t-t-J⊥model for bilayer nickelatesuperconductors.