This review considers the properties of classical solutions to supergravity theories
with partially unbroken supersymmetry. These solutions saturate Bogomol’nyPrasad-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 σ-models; and the target-space geometry of BPS instanton
solutions obtained by the dimensional reduction of static p-branes.