  Optomechanics, the study of the mechanical interaction of light with matter,
has proven to be a fruitful area of research that has yielded many notable
achievements, including the direct detection of gravitational waves in
kilometer-scale optical interferometers. Light has been used to cool and
demonstrate quantum control over the mechanical degrees of freedom of
individual ions and atoms, and more recently has facilitated the observation of
quantum ``mechanics'' in objects of larger mass, even at the kg-scale. Optical
levitation, where an object can be suspended by radiation pressure and largely
decoupled from its environment, has recently established itself as a rich field
of study, with many notable results relevant for precision measurement, quantum
information science, and foundational tests of quantum mechanics and
fundamental physics. This article provides a survey of several current
activities in field along with a tutorial describing associated key concepts
and methods, both from an experimental and theoretical approach. It is intended
as a resource for junior researchers who are new to this growing field as well
as beginning graduate students. The tutorial is concluded with a perspective on
both promising emerging experimental platforms and anticipated future
theoretical developments.
