Artificial neural networks are a neurobiologically inspired paradigm that emulates the functioning of the brain. They are based on neuronal function, because neurons are recognized as the cellular elements responsible for the brain information processing. However, recent studies have demonstrated that astrocytes can signal to other astrocytes and can communicate reciprocally with neurons, which suggests a more active role of astrocytes in the nervous system physiology and fundamental brain functions. This novel vision of the glial role on brain function calls for a reexamination of our current vision of artificial neural networks, which should be expanded to consider artificial neuroglial networks. The neuroglial network concept has not been yet applied to the computational and artificial intelligent sciences. However, the implementation of artificial neuroglial networks by incorporating glial cells as part of artificial neural networks may be as fruitful and successful for artificial networks as they have been for biological networks.