This chapter presents a study that incorporates into the connectionist systems new elements that emulate cells of the glial system. More concretely, we have considered a determined category of glial cells known as astrocytes, which are believed to be directly implicated in the brain’s information processing. Computational models have helped to provide a better understanding of the causes and factors that are involved in the specific functioning of particular brain circuits. The present work will use these new insights to progress in the field of computing sciences and artificial intelligence. The proposed connectionist systems are called artificial neuroglial networks (ANGN).