Electron holography is a powerful technique that allows the phase shift of a high-energy electron wave that has passed through a specimen in the transmission electron microscope to be measured directly. The phase shift can then be used to provide quantitative information about local variations in magnetic field and electrostatic potential both within and surrounding the specimen. This chapter begins with an outline of the experimental procedures and theoretical background that are needed to obtain phase information from electron holograms. It then presents recent examples of the application of electron holography to the characterization of magnetic domain structures and electrostatic fields in nanoscale materials and working devices, including arrangements of closely spaced nanocrystals, patterned elements and nanowires, and electrostatic fields in field emitters and doped semiconductors. The advantages of using digital approaches to record and analyze electron holograms are highlighted. Finally, high-resolution electron holography, alternative modes of electron holography and future prospects for the development of the technique are briefly outlined.