An alternans rhythm consists on the beat to beat oscillation in the duration of cardiac electrical excitation, that is thought to be linked to the onset of ventricular fibrillation, through its destabilizing effect on spiral or scroll waves formed on cardiac muscle. We show that the spatio-temporal dynamics of cardiac alternans can be well described by a Ginzburg-Landau type equation. These results agree well with those obtained from numerical simulations of detailed ionic models, and reproduce the experimentally observed dynamics. Furthermore, we have used our simplified model to study control of spatially extended alternans from a single site. This analysis reveals that control failure above a critical cable length is caused by the formation of standing wave patterns of alternans that are eigenfunctions of a forced Helmotz equation. Recent experiments of control in linear strands of tissue confirm our theoretical results.