（ABSTRACT）

Kaluza-Klein consistent truncations from the D=10, 11 supergravities down to lower-dimensional (gauged) supergravities have been traditionally thought to be possible only in very exceptional circumstances. Here we will review recent progress in the construction of consistent truncations on wide classes of internal spaces down to D=4, 5 minimal (pure) gauged supergravities. Moreover, we will show that, under certain conditions, massive modes up the Kaluza-Klein tower can, against the standard lore, be consistently retained to yield D=4, 5 matter-coupled supergravities. We will conclude with an AdS/CMT application, constructing an M-theory background with Lifshitz symmetry.