A conspicuous ability of the mammalian brain to integrate and process huge amount of spatial, visual and temporal stimuli is a result of its enormous structural complexity functioning in an integrated way as a whole. Here we review recent achievements in the understanding of brain structure and function. A traditional view on the brain as a network of neurons has been extended to the more complicated structure including overlapping and interacting networks of neurons and glial cells. We discuss artificial versus natural neural networks and consider a concept of attractor networks. Moreover, we speculate that each neuron can have an intracellular network on a genetic level, based and functioning on the principle of artificial intelligence. Hence, we speculate that mammalian brain is, in fact, a network of networks. We review different aspects of this structure and propose that the study of brain can be successful only if we utilize the concepts recently developed in nonlinear dynamics: the concept of integrated information, emergence of collective dynamics and taking account of unexpected behavior and regimes due to nonlinearity. Additionally, we discuss perspectives of medical applications to be developed following this research direction.