  This review considers the properties of classical solutions to supergravity
theories with partially unbroken supersymmetry. These solutions saturate
Bogomol'ny-Prasad-Sommerfield bounds on their energy densities and are the
carriers of the $p$-form charges that appear in the supersymmetry algebra. The
simplest such solutions have the character of $(p+1)$-dimensional
Poincar\'e-invariant hyperplanes in spacetime, i.e. $p$-branes. Topics covered
include the relations between mass densities, charge densities and the
preservation of unbroken supersymmetry; interpolating-soliton structure;
diagonal and vertical Kaluza-Klein reduction families; multiple-charge
solutions and the four D=11 elements; duality-symmetry multiplets; charge
quantisation; low-velocity scattering and the geometry of worldvolume
supersymmetric $\sigma$-models; and the target-space geometry of BPS instanton
solutions obtained by the dimensional reduction of static $p$-branes.
