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The notion of nonreciprocity, in essence when going forwards is different from going backwards, emerges in all branches of physics from cosmology to electromagnetism. Intriguingly, the breakdown of reciprocity is typically associated with extraordinary phenomena, which may be readily capitalized on in the design of (for example) nontrivial electromagnetic devices when Lorentz reciprocity is broken. However, in order to enable the exploitation of nonreciprocal-like effects in the next generation of quantum technologies, basic quantum optical theories are required. Here we present a versatile model describing a pair of driven-dissipative quantum resonators, where the relative phase difference between the coherent and incoherent couplings induces an asymmetry. The interplay between the diverse dissipative landscape - which encompasses both intrinsic losses and dissipative couplings - and the coherent interactions leads to some remarkable consequences including highly directional (or even one-way) energy transport. Our work proffers the tantalizing prospect of observing dissipation-induced quantum directionality in areas like photonics or cavity magnonics (spin waves), which may aid the design of unconventional nanoscopic devices.