Superconductivity results from condensation of a macroscopic number of Cooper pairs, which are bound states of electrons. The only generally accepted mechanism of Cooper pairing in metals, which can overcome the Coulomb repulsion of two electrons in a vacuum, is the interaction of electrons with the lattice vibrations. Such electron-phonon mechanism generally leads to s-wave symmetry of the Cooper pair wave function, and is an important part of the Bardeen-Copper-Schrieffer theory of superconductivity. In many poorly understood materials of interest today--including high temperature superconductors based on copper (and perhaps also based on iron)--the Cooper pairing appears in a higher angular momentum channel, for example d-wave. This hints at a different mechanism of superconductivity. This talk will be about some recent progress towards answering the question: "Can superconductivity arise from pure electron-electron repulsion, without any coupling to lattice vibrations? And if yes, what is the mechanism?