  We present a detailed theoretical description of quantum coherent electron
transport in voltage-biased cross-like Andreev interferometers. Making use of
the charge conjugation symmetry encoded in the quasiclassical formalism, we
elucidate a crucial role played by geometric and electron-hole asymmetries in
these structures. We argue that a non-vanishing Aharonov-Bohm-like contribution
to the current $I_S$ flowing in the superconducting contour may develop only in
geometrically asymmetric interferometers making their behavior qualitatively
different from that of symmetric devices. The current $I_N$ in the normal
contour -- along with $I_S$ -- is found to be sensitive to phase-coherent
effects thereby also acquiring a $2\pi$-periodic dependence on the Josephson
phase. In asymmetric structures this current develops an odd-in-phase
contribution originating from electron-hole asymmetry. We demonstrate that both
phase dependent currents $I_S$ and $I_N$ can be controlled and manipulated by
tuning the applied voltage, temperature and system topology, thus rendering
Andreev interferometers particularly important for future applications in
modern electronics.
