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The MAB phases are atomically layered, ternary or quaternary transition metal (M) borides (TMBs), with the general formula (MB)_{2 z}A_x(MB₂)_y( z = 1–2; x = 1–2; y = 0–2), whose structures are composed of a transition M-B sublattices interleaved by A-atom (A = Al,Zn) mono- or bilayers. Most of the MAB phases were discovered before the 1990s, but recent discoveries of intriguing magnetocaloric properties, mechanical deformation behaviour, catalytic properties, and high-temperature oxidation resistance has led to their ‘re-discovery’. Herein, MAB phase synthesis is reviewed and their magnetic, electronic, thermal, and mechanical properties are summarized. Because the M-B layers in the MAB phases structurally resemble their corresponding binaries of the same M:B stoichiometry, the effects of the A-layers on properties are discussed. Inconsistencies in the literature are critically assessed to gain insights on the processing-structure-property relations, suggest fruitful avenues for future research, and identify limitations for prospective applications.