An FGM (Fano-Gushel-Mukai) variety of dimension n has a semiorthogonal decomposition consisting of 2n-4 exceptional bundles and a complementary category. The properties of the complementary category depend on n in a funny way. When n is even it is of K3 type (with Serre functor equal to the shift by 2 and Hochschild homology of dimension 24) and when n is odd it is of “Enriques type” (with Serre functor equalt to the shift by 2 composed with an involution). In particular, an FGM fourfold is very similar to the cubic fourfold. I will discuss a strange “duality” on the set of all FGM varieties and a relation between derived categories of dual FGMs. This is a joint work in progress with Alex Perry.