The low energy effective action of M theory is eleven dimensional supergravity. Higher order corrections start at order R^4 and have many applications, for example, to testing microsopic M theory models.

      I shall review what is known about R^4 terms in M theory and string theory and discuss various approaches that can be taken to finding the full action. In particular, I shall show how deformations of maximally supersymmetric field theories can be understood in terms of certain spinorial cohomology groups which can be defined in superspace. The formalism will be illustrated in D=10 SYM theory. As an aside I shall show how spinorial cohomology is related to pure spinor cohomology. The D=11 case will then be discussed and an action formula for the R^4 invariant derived.