The Tweedie compound Poisson distribution is a mixture of a degenerate distribution at the origin and a continuous distribution on the positive real line. It has been applied in a wide range of fields in which continuous data with exact zeros regularly arise. The cplm package provides likelihood based and Bayesian procedures for fitting common Tweedie compound Poisson linear models. In particular, models with hierarchical structures or extra zero inflation can be handled. Further, the package implements the Gini index based on an ordered version of the Lorenz curve as a robust model comparison tool involving zero-inflated and highly skewed distributions.