During inspection of a sample with an electron beam, either in a scanning electron microscope or an electron microprobe, x-rays characteristic of the elements making up the sample are generated.  These x-rays can be detected with either an energy dispersive spectrometer (EDS) or a wavelength dispersive spectrometer (WDS).  Analyses can be made on a point by point basis or can be acquired in mapping fashion. 
 
EDS systems are typically found on Scanning Electron Microscopes (SEM).
 
WDS systems are typically found on Electron Microprobes (EMA).