Context. Recent studies of low- and intermediate-mass stars show that the evolution of the chemical elements in these stars is very different from that proposed by standard stellar models. Rotation-induced mixing modifies the internal chemical structure of main sequence stars, although its signatures are revealed only later in the evolution when the first dredge-up occurs. Thermohaline mixing is likely the dominating process that governs the photospheric composition of low-mass red giant branch stars and has been shown to drastically reduce the net 3He production in these stars. The predictions of these new stellar models need to be tested against galaxy evolution. In particular, the resulting evolution of the light elements D, 3He and 4He should be compared with their primordial values inferred from the Wilkinson Microwave Anisotropy Probe data and with the abundances derived from observations of different Galactic regions. Aims: We study the effects of thermohaline mixing and rotation-induced mixing on the evolution of the light elements in the Milky Way. Methods: We compute Galactic evolutionary models including new yields from stellar models computed with thermohaline instability and rotation-induced mixing. We discuss the effects of these important physical processes acting in stars on the evolution of the light elements D, 3He, and 4He in the Galaxy. Results: Galactic chemical evolution models computed with stellar yields including thermohaline mixing and rotation fit better observations of 3He and 4He in the Galaxy than models computed with standard stellar yields. Conclusions: The inclusion of thermohaline mixing in stellar models provides a solution to the long-standing "3He problem" on a Galactic scale. Stellar models including rotation-induced mixing and thermohaline instability reproduce also the observations of D and 4He.