Neurologically related injuries cause a similar number of deaths as cancer, and brain damage is the second commonest cause of death in the world and probably the leading cause of permanent disability. The devastating effects of most cases of brain damage could be avoided if it were detected and medical treatment initiated in time. The passive electrical properties of biological tissue have been investigated for almost a century and electrical bioimpedance studies in neurology have been performed for more than 50 years. Even considering the extensive efforts dedicated to investigating potential applications of electrical bioimpedance for brain monitoring, especially in the last 20 years, and the specifically acute need for such non-invasive and efficient diagnosis support tools, Electrical Bioimpedance technology has not made the expected breakthrough into clinical application yet. In order to reach this stage in the age of evidence-based medicine, the first essential step is to demonstrate the biophysical basis of the method under study. The present research work confirms that the cell swelling accompanying the hypoxic/ischemic injury mechanism modifies the electrical properties of brain tissue, and shows that by measuring the complex electrical bioimpedance it is possible to detect the changes resulting from brain damage. For the development of a successful monitoring method, after the vital biophysical validation it is critical to have available the proper electrical bioimpedance technology and to implement an efficient protocol of use. Electronic instrumentation is needed for broadband spectroscopy measurements of complex electrical bioimpedance; the selection of the electrode setup is crucial to obtain clinically relevant measurements, and the proper biosignal analysis and processing is the core of the diagnosis support system. This work has focused on all these aspects since they are fundamental for providing the solid medico-technological background necessary to enable the clinical usage of Electrical Bioimpedance for cerebral monitoring.