It has been known for a long time that a large fraction of disc galaxies are lopsided. We simulate three different mechanisms that can induce lopsidedness: flyby interactions, gas accretion from cosmological filaments and ram pressure from the intergalactic medium. Comparing the morphologies, H i spectrum, kinematics and m= 1 Fourier components, we find that all of these mechanisms can induce lopsidedness in galaxies, although in different degrees and with observable consequences. The time-scale over which lopsidedness persists suggests that flybys can contribute to ∼20 per cent of lopsided galaxies. We focus our detailed comparison on the case of NGC 891, a lopsided, edge-on galaxy with a nearby companion (UGC 1807). We find that the main properties of NGC 891 (morphology, H i spectrum, rotation curve, existence of a gaseous filament pointing towards UGC 1807) favour a flyby event for the origin of lopsidedness in this galaxy.