  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 some 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.
