Bosons are quantum mechanical particles that follow Bose–Einstein statistics, or equivalently, that possess integer spin. These particles can be classified as elementary: these are the Higgs boson, the photon, the gluon, the W/Z and the hypothetical graviton; or composite like the atom of hydrogen, the atom of O, the nucleus of deuterium, mesons etc. Additionally, some quasiparticles in more complex systems can also be considered bosons like the plasmons (quanta of charge density waves).
The first model that treated a gas with several bosons, was the photon gas, a gas of photons, developed by Bose. This model leads to a better understanding of Plancks law and the black-body radiation. The photon gas can be easily expanded to any kind of ensemble of massless non-interacting bosons. The phonon gas', also known as Debye model, is an example where the normal modes of vibration of the crystal lattice of a metal, can be treated as effective massless bosons. Peter Debye used the phonon gas model to explain the behaviour of heat capacity of metals at low temperature.
An interesting example of a Bose gas is an ensemble of helium-4 atoms. When a system of He atoms is cooled down to temperature near absolute zero, many quantum mechanical effects are present. Below 2.17 kelvins, the ensemble starts to behave as a superfluid, a fluid with almost zero viscosity. The Bose gas is the most simple quantitative model that explains this phase transition. Mainly when a gas of bosons is cooled down, it forms a Bose–Einstein condensate, a state where a large number of bosons occupy the lowest energy, the ground state, and quantum effects are macroscopically visible like wave interference.
The theory of Bose-Einstein condensates and Bose gases can also explain some features of superconductivity where charge carriers couple in pairs (Cooper pairs) and behave like bosons. As a result, superconductors behave like having no electrical resistivity at low temperatures.
The equivalent model for half-integer particles (like electrons or helium-3 atoms), that follow Fermi–Dirac statistics, is called the Fermi gas (an ensemble of non-interacting fermions). At low enough particle number density and high temperature, both the Fermi gas and the Bose gas behave like a classical ideal gas.