Gerstenhaber's original deformation theory was in terms of the Hochschild cohomology H(A,A). The primary obstruction is given in terms of the Gerstenhaber bracket. Higher order obstructions can be expressed in terms of special Gerstenhaber-Massey multi-brackets. These are related to an sh-Lie structure on H(A,A), which in turn is related to the Grothendieck yoga that deformations are controlled by dg Lie algebras, up to sh-Lie equivalence, cf. Kontsevich's proof that any Poisson manifold can be deformation quantized.