We present here a systematical approach to studying the varying brain. We first distinguish different types of brain variability and provide examples for them. Next, we show classical analysis of covariance (ANCOVA) as well as advanced residual analysis via statistical- and deep-learning aim to decompose the total variance of the brain or behaviour data into explainable variance components. Additionally, we discuss innate and acquired brain variability. For varying \textit{big brain data}, we define the \textit{neural law of large numbers} and discuss methods for extracting representations from large-scale, potentially high-dimensional brain data. Finally, we examine the gut-brain axis, an often lurking, yet important, source of brain variability.