Memristor devices are a promising technology to replace CMOS for neuromorphic computing applications. As an alternative to filament-type memristors that require ‘forming’ procedures and which typically exhibit binary ‘on/off’ switching, we are investigating memristors based on a Li ion intercalation oxide Li_xCoO₂. Our devices are composed of simple structures consisting of Li_xCoO₂ films on insulating substrates with top or bottom contacts of Au. The electronic conductivity of the Li_xCoO₂ film strongly depends on the Li-ion concentration and can exhibit synaptic multilevel analog states. However, determining the precise physical mechanisms that give rise to resistive states within a working device remains a challenge. This challenge arises because bulk characterization techniques (i.e. electrochemical impedance spectroscopy (EIS)) can be insensitive to the details of the materials microstructure that are critical to the device behavior. Scanning probe microscopy offers an attractive route to overcome these limitations in order to better understand transport at interfaces and along nanometer length scales. Here, we have carried out in operando Kelvin probe force microscopy (KPFM) on active Li_xCoO₂ memristor devices. Using KPFM, we have directly imaged the potential drops along the device and determined the resistance of the channel versus resistance at the electrode interfaces. By capturing the time evolution of the potential landscape, the ionic and electronic dynamics are separated and their interdependence is revealed. Localized changes in work function suggest regions of Li accumulation and depletion that are associated with particular resistive memory states. The insights we gain from these experiments will guide the fabrication of more complex memristor devices such as row-column addressable arrays.