Analytical electron microscopy (AEM) refers to a collection of spectroscopic techniques that are capable of providing structural, compositional, and bonding information about samples probed by an electron beam, typically inside a transmission electron microscope (TEM). Several AEM techniques are covered with particular attention given to the EDXS (energy-dispersive x-ray spectroscopy) microanalysis and EELS (electron energyloss spectroscopy) techniques. First, the different AEM techniques available in TEMs are surveyed and a parallel between EELS and EDXS is drawn. A fundamental description of the elastic and inelastic scattering events responsible for these signals is presented. The practical challenges related to electron optics and instrumentation capabilities are then discussed. Technical advances that have affected the performance of these AEM techniques are outlined, including successive generations and technologies of energy filters, monochromators, aberration correctors, and advanced energydispersive x-ray spectrometers. The different approaches of spectroscopic imaging with x-rays and energy-loss spectroscopy, the resolution limits, and the effects of electron-beam propagation are also described along with the types of information that can be extracted with electron-energyloss near-edge structures. After a review of dielectric theory and low-loss spectroscopy, examples of plasmonic imaging are presented. The review also draws attention to the many efforts to extend the limits of spatial resolution and the atomic-level chemical analyses of materials. Some important progress in the statistical analysis of signals and associated numerical methods is mentioned. The review also presents some novel developments in image capture, such as the pixelated detectors. Finally, the realm of phonon spectroscopy made possible through the latest instrumentation is also discussed.