Abstract: We investigated the electron-phonon ( e -ph ) coupling and vibrational thermal conductivity in the representative MAB compounds, namely MoAlB, WAlB, Tc 2 AlB 2 , and Cr 2 AlB 2 . The spectral distribution functions of e -ph interaction, obtained through ab initio linear-response calculations, reveal that the electron-phonon coupling values range from low (0.15) to moderate (0.58). With such e -ph coupling, out of the considered compounds, only Tc 2 AlB 2 exhibits a superconducting transition, at 4 K. We further evaluated the thermal conductivity and associated properties like scattering rates, obtained using ab initio and other methodologies. The latter included the iterative solution of the Peierls-Boltzmann transport equation, using HIPHIVE package for advanced optimization and machine learning techniques, and employing maximum likelihood estimation to approximate scattering rates from a limited set of scattering processes. We found that these methods yield nearly identical predictions for thermal conductivity values, with a significant decrease in the computational cost compared to the first-principles methods. We examined interactions arising from both three-phonon (3 ph ) and four -phonon (4 ph ) scattering processes. The 4 ph interactions demonstrated a smaller yet significant impact on the overall vibrational thermal conductivity, most notably in Tc 2 AlB 2 . Our findings indicate that Cr 2 AlB 2 has the highest thermal conductivity across all considered crystal directions, with the thermal conductivity being spatially anisotropic, most pronouncedly in Tc 2 AlB 2 . Finally, we show that empirical expressions based on Slack models are well suited for screening the thermal conductivity properties of MAB phases, and can be employed to establish upper and lower limits of their thermal conductivity.