In this paper, a summary of the composite models developed for use in actuarial practice is presented. We refer in extensive detail to the first composite model introduced in 2005 by Cooray and Ananda [3] which was then generalized by Scollnik [11] in 2007. The main features identified for these models were the density function, the cumulative distribution function, and the n-th order initial moment. We also look into some different variations of these composite models such as: Gamma -Pareto, Weibull -Pareto and Exponential -Pareto models.