Technological advances in device micro- and nano-fabrication over the past decade has enabled a variety of novel heterojunction device structures to be made. Among these, magnetic multilayers, superconductor/normal metal junctions and carbon nanotubes exhibit a rich variety of features, with the potential for future generations of electronic devices with improved sensitivity and higher packing density. The modeling of such structures in a flexible and accurate way, with a predictive capability is a formidable theoretical challenge. In this thesis I will present a very general numerical technique to compute transport properties of heterogeneous systems, which can be used together with accurate spd tight-binding Hamiltonians or simpler models. I will then apply this technique to several transport problems in the mesoscopic regime. Firstly I will review the material dependence of CPP GMR in perfect crystalline magnetic multilayers, analyze their conductance oscillations and discuss some preliminary results of magnetic tunneling junctions. In the contest of the conductance oscillations I will introduce a simple Kronig-Penney model which gives a full understanding of the relevant periods involved in the oscillations. I will then present a simple model, which can be used to study disordered magnetic systems and the cross-over from ballistic to diffusive transport. This model explains recent experiments on CPP GMR, which cannot be understood within the usual Boltzmann transport framework. Then I will present results for superconducting/normal metal and for superconducting/multilayer junctions. In the case of multilayers I will show that in both the ballistic and diffusive regimes the GMR is expected to vanish if a superconducting contact is added and go on to show why this is not the case in practice. Finally I will present features of ballistic transport in multiwall carbon nanotubes and show how the inter-tube interaction can, not only block some of the scattering channels but also re-distribute non-uniformly the current across the tubes. The results explain an old open question concerning ballistic transport in Carbon nanotubes.