Two examples of muli-level explanations of brain activity are provided. First study is aimed at extraction of information from EEG to recognize which brain regions are active using spectral fingerprinting. It is based on forward and inverse modeling of electric potentials measured by sensors placed on the scalp, and computing power spectra from different brain locations. Reliable recognition of specific brain activity using EEG may lead to better diagnostic and therapeutic methods, and various new ways of building brain-computer interfaces. In the second study, infant EEG data collected at our BabyLAB were used to derive Event-Related Potentials (ERPs), in an oddball paradigm with two types of deviant stimuli (easy and hard) and one standard stimuli. Tensor decomposition of these signals, conforming to non-negative Canonical Polyadic decomposition (NCPD) model and non-negative Tucker decomposition (NTD), is used to characterize differences in processing these stimuli. Multi-domain temporal, spectral, time-frequency representation (TFR) and spatial information features are simultaneously analyzed for more reliable representation of the underlying source of brain activity. Results show right-side asymmetry for 5-frequency (Hz) theta band and may be due to the dynamical process of expectancy and surprise, corresponding to deviant detection reflected in the mismatch response.