We review the derivation of dispersion relations for forward Compton scattering off the nucleon, including the Lorentz decomposition of the Compton tensor $T^{\mu\nu}$. We then discuss the dispersion relations for the resulting scalar functions $T_1$ and $T_2$ and present the consequences in terms of sum rules for the nucleon polarizabilities. Finally, we revisit the Cottingham formula and summarize the present status of its phenomenological evaluation. In particular, we stress that regardless of a fixed pole in $T_1$, the elastic contribution is unambiguous, providing a dispersive definition for the notion of the Born terms.