After presenting an intuitive picture of quasi-particle transport in mesoscopic superconductors, which emphasizes the intimate relation between Andreev scattering and zero resistivity, the authors develop a general theory of DC transport in mesoscopic normal-superconducting structures. Generalized multi-probe conductance formulae are derived, which take into account not only the effect of Andreev scattering on transport coefficients, but also the non-conservation of quasi-particle charge which arises in the presence of a superconducting condensate. Experiments on quasi-particle charge imbalance are described naturally by this approach.