The increasing number of energy filtering transmission electron microscopes (EFTEMs) has given many microscopists the ability to apply the fast and very efficient tool of electron spectroscopic imaging (ESI) for analytical characterisation, rather than to record EELS spectra. In a more general framework, the new ESI methods and the standard PEELS technique both aim at exploring the same three-dimensional data space. This data space is represented by the spatial co-ordinates x, y and the energy loss ΔE. The resulting intensity distribution I(x,y, ΔE) is frequently referred to as a spectrum image and the experimental techniques to acquire the corresponding data are referred to as spectrum imaging. The actual analysis can either be based on recording PEELS spectra for a twodimensional array of probe positions, or on recording series of energy filtered images across inner shell loss edges or in the low loss region.