  The BCS theory of superconductivity named electron-phonon interaction as a
glue that overcomes Coulomb repulsion and binds fermions into pairs which then
condense and superconduct. We review recent and not so recent works aiming to
understand whether a nominally repulsive Coulomb interaction can by itself give
rise to a superconductivity. We first discuss a generic scenario of the pairing
by electron-electron interaction, put forward by Kohn and Luttinger back in
1965, and then turn to modern studies of the electronic mechanism of
superconductivity in the lattice models for the cuprates, the Fe-pnictides, and
the doped graphene. We show that the pairing in all three classes of materials
can be viewed as lattice version of Kohn-Luttinger physics, despite that the
pairing symmetries are different. We discuss under what conditions the pairing
occurs and rationalize the need to do parquet renormalization-group analysis.
We also discuss the interplay between superconductivity and
density-instabilities.
