  The Gerasimov-Drell-Hearn sum rule is one of several dispersive sum rules
that connect the Compton scattering amplitudes to the inclusive photoproduction
cross sections of the target under investigation. Being based on such universal
principles as causality, unitarity, and gauge invariance, these sum rules
provide a unique testing ground to study the internal degrees of freedom that
hold the system together. The present article reviews these sum rules for the
spin-dependent cross sections of the nucleon by presenting an overview of
recent experiments and theoretical approaches. The generalization from real to
virtual photons provides a microscope of variable resolution: At small
virtuality of the photon, the data sample information about the long range
phenomena, which are described by effective degrees of freedom (Goldstone
bosons and collective resonances), whereas the primary degrees of freedom
(quarks and gluons) become visible at the larger virtualities. Through a rich
body of new data and several theoretical developments, a unified picture of
virtual Compton scattering emerges, which ranges from coherent to incoherent
processes, and from the generalized spin polarizabilities on the low-energy
side to higher twist effects in deep inelastic lepton scattering.
