SupOU processes, or superpositions of Ornstein-Uhlenbeck type processes, belong to the class of stationary stochastic processes for which the marginal distribution and dependence structure can be modeled independently. To define them, the concepts of infinite divisibility and Lévy processes are first introduced. Their basic properties are given, and the connection between them is explained. The concept of selfdecomposable random variables is also defined, showing that they constitute the class of marginal distributions of Ornstein-Uhlenbeck type processes. Some basic properties of such processes are discussed, and the supOU process is characterized as an infinite superposition of Ornstein-Uhlenbeck type processes, obtained by randomizing the parameter using a probability measure. To make sense of the integral defined in this way, the concepts of a homogeneous infinitely divisible independently scattered random measure, or Lévy basis, and integration with respect to such a measure are introduced. The formal definition of the supOU process is then stated, followed by the derivation of the cumulant functions of the marginal distributions. The expression for the autocorrelation function of the supOU process is derived, showing that these processes can exhibit long-range dependence. The integrated process is briefly explained as an example important in applications. The definition of the supOU process is generalized to the multidimensional case, for which the conditions under which it has moments of any order are shown, along with expressions for the expectation, variance, and covariance of such a process.