  This review is concerned with the motion of a point scalar charge, a point
electric charge, and a point mass in a specified background spacetime. In each
of the three cases the particle produces a field that behaves as outgoing
radiation in the wave zone, and therefore removes energy from the particle. In
the near zone the field acts on the particle and gives rise to a self-force
that prevents the particle from moving on a geodesic of the background
spacetime. The field's action on the particle is difficult to calculate because
of its singular nature: the field diverges at the position of the particle. But
it is possible to isolate the field's singular part and show that it exerts no
force on the particle -- its only effect is to contribute to the particle's
inertia. What remains after subtraction is a smooth field that is fully
responsible for the self-force. Because this field satisfies a homogeneous wave
equation, it can be thought of as a free (radiative) field that interacts with
the particle; it is this interaction that gives rise to the self-force. The
mathematical tools required to derive the equations of motion of a point scalar
charge, a point electric charge, and a point mass in a specified background
spacetime are developed here from scratch. The review begins with a discussion
of the basic theory of bitensors (part I). It then applies the theory to the
construction of convenient coordinate systems to chart a neighbourhood of the
particle's word line (part II). It continues with a thorough discussion of
Green's functions in curved spacetime (part III). The review concludes with a
detailed derivation of each of the three equations of motion (part IV).
