In the present work, the 204–210Tl isotopes have been investigated by performing large-scale shell-model calculations, including configurations allowing both neutron and proton core excitations across the Z=82 and N=126 shell gaps. Inspired by the recent high-spin experimental data, the structure of Tl isotopes has been studied for a considerably large model space. The KHHE interaction has been used for 204–206Tl isotopes, KHH7B interaction for 204–210Tl isotopes, and additionally KHM3Y interaction has been used for 208Tl isotope. The core excitation has been performed using the KHH7B and KHM3Y interactions. The level spectra of 204–210Tl isotopes are comprehensively described and explained by multi-nucleon couplings of single-particle-hole orbitals within the valence space and by core excitations across 208Pb core. The well-known isomeric states are analyzed in terms of the shell model configurations.