Potential and electrochemical measurements of biological cell electroactivity is crucial in cell biology research. The traditional technique with a micrometer-sharp glass pipette equipped with a metal wire within its core or electrically conductive saline solution allows extracellular, ion-channel and intracellular measurements. In applications that require multichannel measurements, this approach is, however, impractical and planar arrays of metal electrodes are usually employed. Yet, with planar geometry, they allow extracellular measurements only. Several approaches to developing functional three-dimensional electrode arrays with features able to penetrate cell membrane are currently investigated by various groups. While a number of experimental setups have been recently developed, the question remains whether the nanostructure is in fact penetrating the cellular membrane, and if the measurements are indeed intracellular. In my thesis, I approach the problem from two angles. Firstly, I worked on the development of stable and functional three-dimensional electrodes with focus on their electric connectivity, insulation, cell-penetration ability and investigated their electrochemical performance, biocompatibility, and cost-effectiveness of the fabrication. Secondly, I worked on a reliable imaging method that would be able to directly envision nanostructure-cell membrane interface. As a result, a novel maskless patterning method of CNT forests was invented, devices with multichannel arrays of electrodes with silicon nanowires were fabricated and tested, and a reliable FIBSEM method providing three-dimensional images of nanowire- and nanotube-cell interaction and membrane penetration was developed.