Exotic atom
An exotic atom is a normal atom in which one or more sub-atomic particles have been replaced by other particles of the same charge.  For example, electrons may be replaced by other negatively charged particles such as muons or pions, or the positively charged proton which is the nucleus of the hydrogen-1 atom may be replaced by other positively charged particles, or both.  Because these substitute particles are either unstable, interact with the nucleus, or both, exotic atoms have a short half-life.

# Muonic atoms
In a muonic atom, an electron is replaced by a muon, which, like the electron, is a lepton.  Since leptons are only sensitive to weak, electromagnetic and gravitational forces, muonic atoms are governed to very high precision by the electromagnetic interaction.  There are no complications due to strong forces between the lepton and the nucleus.
Since a muon is more massive than an electron, the Bohr orbits are closer to the nucleus in a muonic atom than in an ordinary atom, and corrections due to quantum electrodynamics are more important. Study of muonic atoms' energy levels as well as transition rates from excited states to the ground state therefore provide experimental tests of quantum electrodynamics.
Muon-catalyzed fusion is a technical application of muonic atoms.

# Hadronic atoms
A hadronic atom is an atom in which one or more of the orbital electrons has been replaced by a hadron.  Possible hadrons include mesons such as the pion or kaon, yielding a mesonic atom, antiprotons, yielding a antiprotonic atom, and the Template:SubatomicParticle particle, yielding a Template:SubatomicParticle or sigmaonic atom.
Unlike leptons, hadrons can interact via the strong force, so the energy levels of hadronic atoms are influenced by nuclear forces between the nucleus and the hadron.  Since the strong force is a short-range interaction, these effects are strongest if the atomic orbital involved is close to the nucleus, when the energy levels involved may broaden or disappear because of the absorption of the hadron by the nucleus.  Hadronic atoms, such as pionic hydrogen and kaonic hydrogen, thus provide interesting experimental probes of the theory of strong interactions, quantum chromodynamics.

# Onium
An onium (plural: onia) is the bound state of a particle and its antiparticle. The classic onium is positronium, which consists of an electron and a positron bound together as a long-lived metastable state. Positronium has been studied since the 1950s to understand bound states in quantum field theory. A recent development called non-relativistic quantum electrodynamics (NRQED) used this system as a proving ground.
Pionium, a bound state of two oppositely-charged pions, is interesting for exploring the strong interaction. This should also be true of protonium.  The true analogs of positronium in the theory of strong interactions, however, are not exotic atoms but certain mesons, the quarkonium states, which are made of a heavy quark such as the charm or bottom quark and its antiquark. (Top quarks are so heavy that they decay through the weak force before they can form bound states.) Exploration of these states through non-relativistic quantum chromodynamics (NRQCD) and lattice QCD are increasingly important tests of quantum chromodynamics.
Muonium, despite its name, is not an onium containing a muon and an antimuon, because IUPAC assigned that name to the system of an antimuon bound with an electron.
Understanding bound states of hadrons such as pionium and protonium is also important in order to clarify notions related to exotic hadrons such as mesonic molecules and pentaquark states.

# Hypernuclear atoms
Atoms may be composed of electrons orbiting a hypernucleus that includes strange particles called hyperons. Such hypernuclear atoms are generally studied for their nuclear behaviour, falling into the realm of nuclear physics rather than atomic physics.

# Quasiparticle atoms
In condensed matter systems, specifically in some semiconductors, there are states called excitons which are bound states of an electron and an electron hole.