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The direct electrical interfacing of semiconductor chips with individual nerve cells and with brain tissue is considered. At first, the structure of the cell-chip contact is described and then the electrical coupling is characterized between ion channels, the electrical elements of nerve cells, and transistors and capacitors of silicon chips. On that basis the signal transmission between microelectronics and microionics is implemented in both directions. Simple hybrid neuroelectronic systems are assembled with neuron pairs and with small neuronal networks. Finally, the interfacing with capacitors and transistors is extended to brain tissue on silicon. The application of CMOS chips with capacitively coupled recording and stimulation sites allows an imaging of neuronal activity with high spatiotemporal resolution. Goal of the work in an integration of neuronal network dynamics and digital electronics on a microscopic level for applications in brain research, medical prosthetics and information technology.