Electrical stimulation is a powerful strategy to improve the differentiation of neural stem cells into neurons. Such an approach can be implemented, in association with biomaterials and nanotechnology, for the development of new therapies for neurological diseases, including direct cell transplantation and the development of platforms for drug screening and disease progression evaluation. Poly(aniline):camphorsulfonic acid (PANI:CSA) is one of the most well-studied electroconductive polymers, capable of directing an externally applied electrical field to neural cells in culture. There are several examples in the literature on the development of PANI:CSA-based scaffolds and platforms for electrical stimulation, but no review has examined the fundamentals and physico-chemical determinants of PANI:CSA for the design of platforms for electrical stimulation. This review evaluates the current literature regarding the application of electrical stimulation to neural cells, specifically reviewing: (1) the fundamentals of bioelectricity and electrical stimulation; (2) the use of PANI:CSA-based systems for electrical stimulation of cell cultures; and (3) the development of scaffolds and setups to support the electrical stimulation of cells. Throughout this work, we critically evaluate the revised literature and provide a steppingstone for the clinical application of the electrical stimulation of cells using electroconductive PANI:CSA platforms/scaffolds.