  This review is devoted to the different techniques that have been developed
to compute the coherent transport properties of quantum nanoelectronic systems
connected to electrodes. Beside a review of the different algorithms proposed
in the literature, we provide a comprehensive and pedagogical derivation of the
two formalisms on which these techniques are based: the scattering approach and
the Green's function approach. We show that the scattering problem can be
formulated as a system of linear equations and that different existing
algorithms for solving this scattering problem amount to different sequences of
Gaussian elimination. We explicitly prove the equivalence of the two
formalisms. We discuss the stability and numerical complexity of the existing
methods.
