We introduce a microscopic model which unravels the physical mechanisms responsible for the observed phase diagram of the RVO3 perovskites. It reveals a nontrivial interplay between superexchange, the orbital-lattice coupling due to the GdFeO3-like rotations of the VO6 octahedra, and orthorhombic lattice distortions. We find that the lattice strain affects the onset of the magnetic and orbital order by partial suppression of orbital fluctuations. The present approach also provides a natural explanation of the observed reduction of magnon energies from LaVO3 to YVO3.