The class of ternary carbides and nitrides known as the MAX phases share common unique naonolayered structure and chemical formula Mn+1AXn, where n = 1, 2 or 3, M is and early transition metal, A is an A-group element (mostly IIIA and IVA) and X is either C or N, represent a new class of solids. The main reason for growing interest in MAX phases lies in their unusual, and sometimes unique properties. In general, MAX phases are  elastically stiff, good thermal and electrical conductors, resistant to chemical attack, and have relatively low thermal expansion coefficients, but also relatively soft and most readily machinable, thermal shock resistant and damage tolerant. Therefore, MAX phases are considered to be a good candidate materials for structural applications in extreme environments. This presentation provides an overview of the current understanding of mechanical behavior of MAX phases and their failure and deformation mechanisms, with the special focus on recent advances on micromechanical testing of MAX phases to elucidate their behavior on the single crystal level.