Over mid-ocean ridges, the interaction between the currents and the topography gives rise to complex flows, which drive the transport properties of biogeochemical constituents, and especially those associated with hydrothermal vents, thus impacting associated ecosystems. This paper describes the circulation in the rift valley along the Azores sector of the North Mid-Atlantic Ridge, using a combination of in-situ data from several surveys and realistic high-resolution modeling. It confirms the presence of a mean deep current with an up-valley branch intensified along the right inner flank of the valley (looking downstream), and a weaker down-valley branch flowing at shallower depth along the opposite flank. The hydrographic properties of the rift-valley water, and in particular the along-valley density gradient that results from a combination of the topographic isolation, the deep flow and the related mixing, are quantified. We also show that the deep currents exhibit significant variability and can be locally intense, with typical values greater than 10 cm/s. Finally, insights on the dynamical forcings of the deep currents and their variability are provided using numerical simulations, showing that tidal forcing of the mean circulation is important and that the overlying mesoscale turbulence triggers most of the variability.