Through cardiac looping during embryonic development, paths of flow through the mature heart have direction changes and asymmetries whose topology and functional significance remain relatively unexplored. Here we show, using magnetic resonance velocity mapping, the asymmetric redirection of streaming blood in atrial and ventricular cavities of the adult human heart, with sinuous, chirally asymmetric paths of flow through the whole. On the basis of mapped flow fields and drawings that illustrate spatial relations between flow paths, we propose that asymmetries and curvatures of the looped heart have potential fluidic and dynamic advantages. Patterns of atrial filling seem to be asymmetric in a manner that allows the momentum of inflowing streams to be redirected towards atrio-ventricular valves, and the change in direction at ventricular level is such that recoil away from ejected blood is in a direction that can enhance rather than inhibit ventriculo-atrial coupling. Chiral asymmetry might help to minimize dissipative interaction between entering, recirculating and outflowing streams. These factors might combine to allow a reciprocating, sling-like, 'morphodynamic' mode of action to come into effect when heart rate and output increase during exercise.