Several microanalytical imaging techniques--energy dispersive X-ray detection, parallel electron energy loss spectroscopy, secondary ion mass spectroscopy, photoelectron spectroscopy and XPS) and scanning Auger microscopy--have reached the stage where they are capable of producing images of a surface with a section of a spectrum in each pixel. The resulting image-spectrum is a complex data structure which requires the use of special methodologies if the data are to be interpreted effectively. Appropriate methods have been developed for Earth satellite image processing and are directly applicable to surface microanalysis. The use of scatter diagrams, interactive correlation partitioning, factor and target factor analysis and principal component analysis are outlined in this paper and their application to semiconducting, catalytic and magnetic structures is illustrated. This field of endeavour can be thought of as being the beginning of an area of study which may be called surface chemometrics.