Field ion microscopy (FIM) can be used to study the three-dimensional structure of materials, such as metals and semiconductors, because successive atom layers can be ionized and removed from the surface by field evaporation. The ions removed from the surface by field evaporation can be analyzed chemically by coupling to the microscope a time-of-flight mass spectrometer of single-particle sensitivity, known as the atom probe (AP). This article describes the principles, sample preparation, and quantitative analysis of FIM. It also provides information on the principles, instrument design and operation, mass spectra and their interpretation, and applications of AP microanalysis.