We illustrate how classical chaotic dynamics influences the quantum
properties at mesoscopic scales. As a model case we study semiclassically
coherent transport through ballistic mesoscopic systems within the Landauer
formalism beyond the so-called diagonal approximation, i.e. by incorporating
classical action correlations. In this context we review and explain the two
main trajectory-based methods developed for calculating quantum corrections:
the configuration space approach and the phase space approach that can be
regarded as less illustrative but more general than the first one