A scanning ion-conductance microscope (SICM) has been developed that can image the topography of nonconducting surfaces that are covered with electrolytes. The probe of the SICM is an electrolyte-filled micropipette. The flow of ions through the opening of the pipette is blocked at short distances between the probe and the surface, thus limiting the ion conductance. A feedback mechanism can be used to maintain a given conductance and in turn determine the distance to the surface. The SICM can also sample and image the local ion currents above the surfaces. To illustrate its potential for imaging ion currents through channels in membranes, a topographic image of a membrane filter with 0.80-micrometer pores and an image of the ion currents flowing through such pores are presented.