The human brain is the most sophisticated spatio-temporal learning system, evolved through millions of years. Inspired by principles of information processing in the brain, from genes to neurons and to the whole brain, where spatially distributed areas learn and evolve incrementally at different time scales of nanoseconds, milliseconds, minutes, hours and years, the talk presents a brain-inspired framework called NeuCube for building new types of AI. They are based on spatio-temporal learning and spatio-temporal associative memories, implemented in NeuCube. Applications span from neuroimaging to multisensory streaming data modelling, classification and event prediction, such as dementia and AD, stroke, epilepsy, psychosis and cybersickness.