Kinetic theory describes gases and plasmas as large collections of interacting molecules, from a statistical point of view. Its most famous success, due to Boltzmann, is the first analytic derivation of the monotonicity in time of the entropy.

In most gases of practical interest, e.g. N₂, O₂ or CO₂, molecules are polyatomic: composed of multiple atoms. This geometrical structure induces rotational and vibrational effects, which are a challenge to include in the theory. We present a general framework for modeling polyatomic molecules in kinetic theory, based on elementary physical ideas and formulated in a measure-theoretic setting. We show that within this framework one may adopt different perspectives, each relevant for a different kind of problem (physical modeling, mathematical analysis or numerical simulation), clarifying and unifying the previous approaches in the literature.