We review the theory of the Mikheyev-Smirnov-Wolfenstein effect, in which matter oscillations can greatly enhance ''in vacuo'' neutrino oscillations, and we examine its consequences for the solar neutrino problem. Using a two-flavor model, we discuss the solutions in the ..delta..m/sup 2/-sin/sup 2/2THETA parameter space for the /sup 37/Cl experiment, and describe their predictions for the /sup 71/Ga experiment and for the spectrum of electron-neutrinos arriving at earth. We also comment on the three-flavor case.