Abstract: The atomically laminated layered ternary transition-metal borides (the MAB phases) have demonstrated outstanding properties and have been applied in various fields. Understanding their thermal and mechanical properties is critical to determining their applicability in various fields such as high-temperature applications. To achieve this, we conducted first-principles calculations based on density-functional theory and the quasiharmonic approximation to determine the thermal expansion coefficients, Gruneisen parameters, bulk moduli, hardness, thermal conductivity, electron-phonon coupling parameters, and the structural and vibrational properties of MoAlB, WAlB, Cr2AlB2, and Ti2InB2. We found varying degrees of anisotropy in the thermal expansion and mechanical properties in spite of similarities in their crystal structures. MoAlB has a mild degree of anisotropy in its thermal expansion coefficient (TEC), while Cr2AlB2 and WAlB display the highest level of TEC anisotropy. We assessed various empirical models to calculate hardness and thermal conductivity, and correlated the calculated values with the material properties such as elastic moduli, Gruneisen parameter, Debye temperature, and type of bonding. Owing to their higher Gruneisen parameters, implying a greater degree of anharmonicity in lattice vibrations and lower phonon group velocities, MoAlB and WAlB have significantly lower lattice thermal conductivity values than those of Cr2AlB2 and Ti2InB2. The hardness and lattice thermal conductivity of MAB phases can be predicted with high accuracy if one utilizes an appropriate model.