The mechanisms underlying the production of thoughts by exceedingly complex cellular networks that construct the human brain constitute the most challenging problem of natural sciences. Our understanding of the brain function is very much shaped by the neuronal doctrine that assumes that neuronal networks represent the only substrate for cognition. These neuronal networks however are embedded into much larger and probably more complex network formed by neuroglia. The latter, although being electrically silent, employ many different mechanisms for intercellular signalling. It appears that astrocytes can control synaptic networks and in such a capacity they may represent an integral component of the computational power of the brain rather than being just brain "connective tissue". The fundamental question of whether neuroglia is involved in cognition and information processing remains, however, open. Indeed, a remarkable increase in the number of glial cells that distinguishes the human brain can be simply a result of exceedingly high specialisation of the neuronal networks, which delegated all matters of survival and maintenance to the neuroglia. At the same time potential power of analogue processing offered by internally connected glial networks may represent the alternative mechanism involved in cognition. © 2010 Elsevier B.V.