Proper use of functional neuro-imaging through effective experimental design and modern statistical analysis provides new insights in current brain research. This tutorial has two aims: to describe aspects of this technology to applied statisticians and to provide some statistical ideas to neuroscientists unfamiliar with quantitative analytic methods that accommodate randomness. Introductory background material and ample references to current literature on the physics of magnetic resonance imaging, Fourier methods for image reconstruction and measures of image quality are included. Two of the statistical approaches mentioned here are extensions of established methods for longitudinal data analysis to the frequency domain. A recent case study provides real-world instances of approaches, problems and open questions encountered in current functional neuro-imaging research and an introduction to the analysis of spatial time series in this context.