We consider a two-dimensional Fermi-liquid coupled to low-energy commensurate spin fluctuations. At small coupling, the hole Fermi surface is large and centered around Q = (π, π). We show that as the coupling increases, the shape of the quasiparticle Fermi surface and the spin-fermion vertex undergo a substantial evolution. At strong couplings, g » ω0, where ω0 is the upper cutoff in the spin susceptibility, the hole Fermi surface consists of small pockets centered at (±π/2, ±π/2). The full spin-fermion vertex is much smaller than the bare one, and scales nearly linearly with \q - Q\, where q is the momentum of the susceptibility. At intermediate couplings, there exist both, a large hole Fermi surface centered at (π, π), and four hole pockets, but the quasiparticle residue is small everywhere except for the pieces of the pockets which face the origin of the Brillouin zone. The relevance of these results for recent photoemission experiments in YBCO and Bi2212 systems is discussed. 1 It is a great honor for us to write this paper for a special issue of Physics Reports dedicated to the 80th anniversary of I.M. Lifshitz' day of birth. The physics of high-Tc superconductors has attracted much interest when, unfortunately, I.M. Lifshitz was already not among us. However, the issue of what happens with a Mott-Hubbard insulator upon doping is very closely related to the works of Ilya Mikhailovich on the electron theory of metals and, in particular, on phase transitions in which the topology of the Fermi surface changes.