In this study, a dendrite-free liquid sodium-potassium alloy (NaK) anode with high capacity, a low reduction potential and fast kinetics was paired with two organic polymer cathodes, poly(N-phenyl-5,10-dihydrophenazine) (P1) and poly(hexaazatrinaphthylene) (P2), in metal-ion batteries. A high energy density of 631 W h kg-1 was achieved for one of the polymers (P1) at a discharge current density of 0.2 A g-1 (∼1C rate), while a still impressive specific energy of 443 W h kg-1 was achieved at 20 A g-1 (∼160C rate), which is an unprecedented value for post-lithium battery cathodes. Outstanding power densities of >105 W kg-1 were demonstrated, thus boosting the rate capability of metal-ion batteries to the level of high-power supercapacitors. Moreover, excellent cyclability was demonstrated, with only 11% capacity loss after 10 000 charge/discharge cycles at 10 A g-1 for cathodes based on P2.