  We review modern achievements and problems in physics of the van der Waals
and Casimir forces which arise due to zero-point and thermal fluctuations of
the electromagnetic field between closely spaced material surfaces. This
subject attracted great experimental and theoretical attention during the last
few years because the fluctuation-induced forces find a lot of applications in
both fundamental physics and nanotechnology. After a short introduction to the
subject, we describe main experimental and theoretical results obtained in the
field during the last fifteen years. In the following presentation, we discuss
some of the recent results by the authors and their collaborators which are of
high promise for future developments. Specifically, we consider new features of
the Casimir force acting between a gold sphere and an indium tin oxide plate,
present the experimental and theoretical results on measuring the Casimir
interaction between two gold surfaces by means of dynamic atomic force
microscope, and outline first measurements of the Casimir interaction between
magnetic surfaces and related theory. Special attention is devoted to the
Casimir effect for graphene, which is the prospective material for
microelectromechanical devices of next generations.
