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

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... eters 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 2π-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.