Electroporation is performed in a controlled manner in either individual or multiple biological cells or biological tissue by monitoring the electrical impedance, defined herein as the ratio of current to voltage in the electroporation cell. The impedance detects the onset of electroporation in the biological cell(s), and this information is used to control the intensity and duration of the voltage to assure that electroporation has occurred without destroying the cell(s). This is applicable to electroporation in general. In addition, a particular method and apparatus are disclosed in which electroporation and/or mass transfer across a cell membrane are accomplished by securing a cell across an opening in a barrier between two chambers such that the cell closes the opening. The barrier is either electrically insulating, impermeable to the solute, or both, depending on whether pore formation, diffusive transport of the solute across the membrane, or both are sought. Electroporation is achieved by applying a voltage between the two chambers, and diffusive transport is achieved either by a difference in solute concentration between the liquids surrounding the cell and the cell interior or by a differential in concentration between the two chambers themselves. Electric current and diffusive transport are restricted to a flow path that passes through the opening.