The first two decades of the 21st century have seen great advances in artificial intelligence and machine learning. The techniques have found their way into everyday life, for example in smartphones, search engines, digital customer assistants, motion control systems, and biomedical devices. The aims of this paper are to outline the possibilities for using artificial intelligence and machine learning techniques in supporting the diagnosis and treatment of neurological diseases, and to discuss selected applications of these techniques based on the most recent published reports. First, contemporary definitions of artificial intelligence and machine learning are presented. This is followed by a review of the most important techniques for intelligent data processing: search methods, mathematical logic, probabilistic methods, classifiers, and artificial neural networks (including deep and convolutional networks). Areas of application of these techniques in medicine are identified, including disease diagnosis and support of treatment as well as monitoring and prediction of changes in health status. The role of artificial intelligence and machine learning in neuroscience is presented, together with examples of diagnostic applications based on anatomical, morphological and functional brain connectivity data. Sample applications of intelligent techniques in supporting the treatment (including surgical management) of nervous system diseases are also described. Ambient smart devices monitoring the health status of patients with chronic neurological conditions are discussed, and selected projects based on smart techniques to support early detection of symptoms of neurodegenerative disorders are described. The conclusions highlight the potential of the techniques, as well as the challenges and risks associated with them. A possible synergy between intelligent systems and actions taken by medical staff is outlined as a way to improve the safety and quality of life of patients with acute and chronic neurological diseases.