Since MAB (where M is a transition metal, A is an groups 13–16 element, and B is boron) phases possess good electrical conductivity, high-temperature oxidation and shock resistance, it is meaningful to develop a database to help us figure out optimal compositions and further promote their applications. In this paper, we screened and studied all the available MABs with the M-site being one of the 3d, 4d, or 5d transition metals by using an ab initio method. Among them, 23 MAB phases of M₂Al₂B₂ (222-MAB phases with M = Ti, V, Nb, Ta, Cr, Mo, W, Mn, and Tc) and M₂AlB₂ (212-MAB phases with M = Sc, Ti, Zr, Hf, V, Nb, Cr, Mo, W, Mn, Tc, Fe, Co, and Ni) stand out in terms of structural stability and their electronic, mechanical, optical and thermodynamic properties have been investigated. For both types of MAB phases early transition elements are more feasible to synthesize than post transition elements, because of the lower number of valence electrons and lower formation energy. The effect of valence electron concentration and composition of MAB compounds could also enable fine tuning of their mechanical properties. The bulk modulus, shear modulus, and Young's modulus of the 222-MAB phases are in the range of 145–233 GPa, 101–145 GPa, and 252–361 GPa, respectively, while they are 152–262 GPa, 91–177 GPa, and 237–422 GPa for the 212-MAB phases, respectively. Their mechanical ductilities also show strong valence electron number dependency, with their maximum value occurring at Ni₂AlB₂ and Co₂AlB₂, respectively. More interestingly, a low thermal expansion coefficient and good high temperature strength have also been found in those MAB phases, which are favorable for their potential applications as refractory materials. In addition, the possibility of forming new two-dimensional (2D) materials from layered MAB phases, termed MBenes, is predicted by investigating the interplay of the tensile strain, complex chemical bonding and exfoliation energy.