Electrical Impedance Tomography (EIT) is a fast, portable imaging technique that produces tomographic images of the internal impedance of an object from surface electrode measurements. This thesis reports the first use of EIT to image evoked brain activity in adults and neonates and determines whether accurate EIT images could be obtained from the adult and neonatal brain. In addition, a realistic head-tank phantom was developed to test the performance of EIT with known impedance changes placed within a real human skull. Two EIT systems were used. Images were obtained using 31 or 21 Ag/AgCl EEG scalp electrodes in adults and neonates, respectively, with either 256 or 187 individual impedance measurements from different electrode combinations: 2 applied a safe, alternating current and 2 measured the resultant scalp voltage. Imaging was performed using a block design with 6-15 stimulation periods of between 10-75s during either: 1) Visual, 2) Somatosensory or 3) Motor stimuli. Impedance changes were detected in 38/39 adults and 9/9 neonates within 0.6-5.8s after stimulus onset, and returned to baseline 7.6-36s after stimulus cessation. Reconstructed images were noisy: -20-70% images showed correct localisation to the expected area of cortex stimulated by the visual, motor or somatosensory paradigms. As EIT images from the head-tank localised changes within 10% of the impedance perturbation, this indicated that poor localisation in humans was not due to the head-shape or the skull, but may be related to unknown physiological factors. An improved EIT reconstruction algorithm, using a computerised finite-element model of the head, showed improved localisation for the adult images. This is the first demonstration that EIT can detect and image impedance changes in the head, probably due to increased regional cerebral blood volume in the activated cortex. Improvements may enable more accurate neuroimaging of the adult and neonatal brain for use in clinical practice.