Time-varying energy profiles of renewable sources, electric vehicles, end user demands, portable devices, novel military applications and more, require high power as well as high energy density in storage systems. Electrochemical capacitors (EECs), with higher power than batteries, benefit from nanostructured geometries that further increase their power capability. Nanostructured electrostatic capacitors (ESCs) are known to have much higher power capability than EECs, though lower energy density. The physical and chemical mechanisms by which EECs and ESCs function in charge/discharge are completely different, as are their electrical specifications and constraints. We consider for the first time how the contrasting characters of electrochemical and electrostatic nanostructured capacitors might be combined in a heterogeneous hybrid circuit to achieve better power and energy performance than either device alone. While the benefits of hybrid circuits have been previously considered for electrochemical devices – i.e., battery and electrochemical capacitor – this perspective article demonstrates for the first time that hybrid storage circuits of heterogeneous devices can exploit the very high power of electrostatic devices, in concert with electrochemical devices. Using response surface models from our own experimental results with nanostructured ESC and ECC devices, we develop a hybrid simulation model combining the two types of devices, recognizing the intrinsic nonlinearities and constraints of each. We demonstrate that charge capture by the ESC and subsequent rapid transfer to the ECC compensates for the lower power capability of the ECC while avoiding energy loss by ESC leakage currents. Although more sophisticated models and simulations are warranted in the future, these initial results underscore the opportunity that ESC devices and hybrid circuits offer for storage applications which require ultrahigh power performance.