Abstract: Vector bundles on a smooth projective variety whose direct image under a general projection to the projective space of the same dimesnion are called Ulrich bundles. The existence of stable Ulrich bundles on projective varieties has been a subjct of much research in the past. We discuss geometry of these bundles on cubic and K3 surfaces. The existence of stable Ulrich bundles on some special hypersurfaces in same as existence of irreducible representations of Clifford algebras. We will discuss this connection as well.