  We review the effects of heavy scalar fields during inflation in the
framework of $\mathcal N = 1$ supergravity. Such heavy scalars can be geometric
moduli from string compactifications or stabilizer fields from a different
sector of the theory. Even when these fields are heavier than the Hubble scale
during inflation, they generically cause backreactions which alter the dynamics
of the system. Severe problems may arise when the heavy fields break
supersymmetry, which is quite generic for K\"ahler moduli. We illustrate these
effects in two examples, chaotic inflation and Starobinsky-like inflation. In
chaotic inflation the backreaction of heavy K\"ahler moduli causes a flattening
of the quadratic potential. In many setups of Starobinsky-like inflation,
however, backreactions spoil the flatness of the plateau.
