The electrical interfacing of individual nerve cells and semiconductor microstructures as well as the assembly of neuronal networks and microelectronic circuits, is considered. At first the planar core-coat conductor of a neuron-silicon junction is studied as it determines the coupling of ion-conducting neurons and electron-conducting silicon. The width of the cleft between cell and chip, the resistance of cleft and voltage-gate ion channels in the junction are investigated. On that basis, a subsequent section describes the electronic interfacing of individual cultured neurons with silicon microstructures as well as the integration of microelectronics with small neuronal networks grown in culture. In a final part, the electronic interfacing of cultured brain slices is addressed. The goal of this approach is an integration of neuronal network dynamics and digital computation on a microscopic level for studies in brain research, biosensorics, information technology and medical prosthetics.