The superform construction of supersymmetric invariants, which consists of integrating the top component of a closed superform over spacetime, is reviewed. The cohomological methods necessary for the analysis of closed superforms are discussed and so
me further theoretical developments presented. The method is applied to higher-order corrections in heterotic string theory up to $a^3$. Some partial results on $N=2,d=10$ and $N=1,d=11$ are also given.
