The talk presents a brief overview of contemporary methods for neurocomputation, including: evolving connections systems (ECOS) and evolving neuro-fuzzy systems [1]; evolving spiking neural networks (eSNN) [2-5]; evolutionary and neurogenetic systems [6]; quantum inspired evolutionary computation [7,8]; rule extraction from eSNN [9]. These methods are suitable for incremental adaptive, on-line learning from spatio-temporal data and for data mining. But the main focus of the talk is how they can learn to predict early the outcome of an input spatio-temporal pattern, before the whole pattern is entered in a system. This is demonstrated on several applications in bioinformatics, such as stroke occurrence prediction, and brain data modeling for brain-computer interfaces [10], on ecological and environmental modeling [11]. eSNN have proved superior for spatio-and spectro-temporal data analysis, modeling, pattern recognition and early event prediction as outcome of recognized patterns when partially presented.