  We review recent developments in the research of nonlinear and nonequilibrium
phenomena in solids focusing on their geometrical aspects. We start with
introducing the basic concepts of geometrical phases of Bloch electrons and
Floquet theory for periodically driven systems. Then we review recent attempts
to engineer topological phases in nonequilibrium matters such as graphene,
magnets, and superconductors irradiated with circularly polarized light. We
next review a bulk photovoltaic effect of inversion broken materials focusing
on the shift current response. The shift current is described with Berry
connections and has a close relationship to the modern theory of polarization.
We further review recent extensions of the shift current to correlated electron
systems. Finally, we explain the geometric diabatic time evolution in the Zener
tunneling process and its consequences on nonreciprocal transport.
