Recent surveys indicate coherent large-scale peculiar motions, commonly referred to as ‘dark flows’, considerably stronger than expected. At the same time, an increasing number of reports suggest the presence of a weak dipolar anisotropy in the supernova data. The Universe seems to accelerate slightly faster in one direction and equally slower in the opposite. Also, this ‘cosmological axis’ lies fairly close to the cosmic microwave background dipole. Since apparent, dipole-like, anisotropies are the trademark signature of peculiar motions, we consider the possibility that these, seemingly unconnected, observations are actually related. In the process, we find that observers living inside a dark flow could experience locally accelerated expansion in a globally decelerating Universe. Moreover, to these observers, the acceleration should appear slightly faster in one direction and equally slower in the opposite, as if there is a preferred axis in the universe. When combined, these results open, in principle at least, the theoretical possibility of addressing the supernova data and the cosmic acceleration by appealing to dark flows rather than dark energy.