Red-giant stars are emerging as one of the most interesting areas of space asteroseismology. Even a relatively basic analysis leads to the determination of the global parameters of the stars, such as their mass and radius, and the very extensive space-based data now available for a large number of stars allow detailed investigation of the deep interiors of red giants, including distinguishing between stars that do and do not have helium fusion in the core, on the basis of periods of gravity waves partially trapped in the core. Here I review the theoretical background for these new developments and provide a simple explanation for the effect on the period spacing of central helium fusion.

This chapter has been prepared for publication in "Asteroseismology", Canary Islands Winter School of Astrophysics, Volume XXII, edited by Pere L. Pall\'e, published by Cambridge University Press