The relation between individual neurons and neuronal networks in performing brain functions is one of the central questions in modern neuroscience. Most of the current literature suggests that the role of individual neurons is negligible and neural networks play a dominant role in the functioning of the nervous system. Individual neurons are usually viewed as network elements whose functions are limited to generating electrical signals and releasing neurotransmitters. Here I summarize experimental evidence that challenges this concept and argue that the unique, intrinsic properties of highly specialized individual neurons are as important for the functioning of the brain as the network properties. I first discuss the studies of relatively 'simple' functions of the nervous system, such as the control of rhythmic 'automatic' movements and generation of circadian rhythm, which indicate that individual neurons may continue performing their functions after being separated from corresponding networks. I then argue that the complex cognitive functions, such as declarative memory, language processing, and face recognition, are likely to be underlain by the properties of groups of highly specialized neurons. These neurons appear to be genetically predisposed to perform cognitive functions and their dysfunctions cannot be compensated by other elements of the nervous system. Under this concept, the electrical signals circulating within and between neural networks are considered to be a means of forming coordinated dynamic ensembles of neurons involved in performing specific functions. While still speculative, this hypothesis may provoke new approaches to studies of neural mechanisms underpinning cognitive functions of the brain.