Cell sorting is an important laboratory process with medical and biotechnological research applications, but a problem common to many current techniques is the contamination of sorted populations with other non-target cells, which limits the usefulness of recovered populations. Microfluidic devices enable new methods of handling minute volumes of biological and chemical samples, including single cells. This work explores techniques for the manipulation of single cells and particles in a microfluidic channel using electrokinetic forces, intended for the isolation of cells from a heterogeneous population and recovery with a high purity. Real-time image processing techniques have been used with an automated control system to sort fluorescent cells and particles using dielectrophoresis as they flow through a microfluidic channel. The use of image data enabled more complex decision algorithms to be used to distinguish between target and non-target particles. Multiple single cells and particles were tracked simultaneously, and identified by their colour, luminosity, size and shape. Several novel electrode geometries have been developed for the manipulation of single cells and particles using dielectrophoresis. Ring electrodes have been used for trapping single cells and particles, and are suitable for massively-parallel and arrayed operation. Minority subpopulations have been enriched by using the traps to select single cells from the bulk population, and recovered with 100\% purity. This method of sorting cells is advantageous if further processing or analysis is intended within the microfluidic device, as cells are volumetrically concentrated as well as being enriched. Dielectrophoretic sorting gates have been developed for sorting particles by deflecting them laterally as they flow through a microfluidic channel junction, with up to five spatially separated outputs. Sorting performance has been characterised by measuring the velocity at which synthetic particles break-through the dielectrophoretic barriers, and the maximum rate at which particles can be sorted. The purity of recovered populations is related to the flow velocity and particle concentration during sorting, and 100\% purity has been obtained for populations sorted at rates of up to 0.9 particles per second.