  Nanomechanics has brought mesoscopic physics into the world of vibrations.
Because nanomechanical systems are small, fluctuations are significant, the
vibrations become nonlinear already for comparatively small amplitudes, and new
mechanisms of dissipation come into play. At the same time, the exquisite
control of these systems makes them a platform for studying many problems of
classical and quantum physics far from thermal equilibrium in a
well-characterized setting. This review describes, at a conceptual level, basic
theoretical ideas and explicative experiments pertaining to mesoscopic physics
of nanomechanical systems. Major applications of nanomechanics in science and
technology are also outlined. A broad range of phenomena related to the
conservative as well as dissipative nonlinearity and fluctuations are discussed
within a unifying framework. They include the linear response of single and
coupled vibrational modes as well as nonlinear effects of periodic driving.
Such driving breaks the continuous time-translation symmetry and the detailed
balance, with conspicuous consequences for fluctuations, particularly in the
presence of the driving-induced bi- and multistability. Mathematical techniques
are described in the appendices to streamline the reading, but also to provide
an introduction to the theory. The goal of the review is to show the richness
of the physics at work. The continuous experimental and theoretical advances
make nanomechanical systems a vibrant area of research, with many new phenomena
to discover.
