This paper reviews recent developments in the still-off-the-mainstream information and data processing area of spiking neural networks (SNN)-the third generation of artificial neural networks. We provide background information about the functioning of biological neurons, discussing the most important and commonly used mathematical neural models. Most relevant information processing techniques, learning algorithms, and applications of spiking neurons are described and discussed, focusing on feasibility and biological plausibility of the methods. Specifically, we describe in detail the functioning and organization of the latest version of a 3D spatio-temporal SNN-based data machine framework called NeuCube, as well as it's SNN-related submodules. All described submodules are accompanied with formal algorithmic formulations. The architecture is highly relevant for the analysis and interpretation of various types of spatio-temporal brain data (STBD), like EEG, NIRS, fMRI, but we highlight some of the recent both STBD-and non-STBD-based applications. Finally, we summarise and discuss some open research problems that can be addressed in the future. These include, but are not limited to: application in the area of EEG-based BCI through transfer learning; application in the area of affective computing through the extension of the NeuCube framework which would allow for a biologically plausible SNN-based integration of central and peripheral nervous system measures. Matlab implementation of the NeuCube's SNN-related module is available for research and teaching purposes. Keywords Artificial neural networks • Spiking neural networks • Spike encoding • Spike-timing dependent plasticity • Spatio-temporal brain data • NeuCube