An exotic atom is a system in which either the nucleus of a hydrogen atom is replaced by an exotic particle (such as a muon, to form muonium, or a positron, to form positronium), or one electron in an ordinary atom is replaced by an exotic particle (such as a muon, pion, or antiproton), or even both substitutions are made (as in antihydrogen). This article deals with those exotic atoms in which a normal nucleus is orbited by electrons and one exotic particle. Atoms of this kind are formed by stopping exotic particles, usually produced in particle accelerators, in matter. The stopped particle replaces an electron in an ordinary atom (Fig. 1). The first orbit of the exotic particle after capture is very similar in size to that of the electron before ejection. Afterward, it cascades down the ladder of exotic-atom states by x-ray and Auger transitions (that is, ejection of electrons). If the exotic particle is a muon, it reaches the lowest energy level, 1s. The muon experiences only the Coulomb interaction with the protons in the nucleus and the weak interaction with all the nucleons. In the case of the hadrons (such as the pion, kaon, or antiproton) the cascade ends earlier for all exotic atoms except those with atomic number 1 or 2, due to nuclear absorption or annihilation of the particle by the short-range strong interaction. Since exotic particles are all much heavier than the electron, they are more strongly bound to the nucleus than electrons, and their transitions during the deexcitation are much more energetic than those of electrons. In addition, exotic particles may come much closer to the nucleus than the electrons in an ordinary atom.