We give an overview of various composite BPS configurations of string theory and M-theory p-branes represented as classical supergravity solutions. Type II string backgrounds can be obtained by S- and T- dualities from NS-NS string - 5-brane configurations corresponding to exact conformal sigma models. The single-center solutions can be also generated from the Schwarzschild solution by applying a sequence of boosts, dualities and taking the extremal limit. Basic `marginal' backgrounds representing threshold BPS bound states of branes are parametrised by a number of independent harmonic functions. `Non-marginal' BPS configurations in D=10 can be constructed from marginal ones by using U-duality and thus depend also on a number of O(d,d) and SL(2,R) parameters. We present a new more general class of configurations in which some of the branes or their intersections are localised on other branes. In particular, we find the type IIB supergravity background describing the BPS configuration of a 3-brane, RR 5-brane and NS-NS 5-brane, and related `localised' 2-5-5 D=11 solution. We also consider the classical action for a 3-brane probe moving in such backgrounds and determine the structure of the corresponding moduli space metrics.