Statistical independence and conditional independence are two fundamental concepts in statistics and machine learning. Copula Entropy is a mathematical concept defined by Ma and Sun for multivariate statistical independence measuring and testing, and also proved to be closely related to conditional independence (or transfer entropy). As the unified framework for measuring both independence and causality, CE has been applied to solve several related statistical or machine learning problems, including association discovery, structure learning, variable selection, and causal discovery. The nonparametric methods for estimating copula entropy and transfer entropy were also proposed previously. This paper introduces copent, the R package which implements these proposed methods for estimating copula entropy and transfer entropy. The implementation detail of the package is introduced. Three examples with simulated data and real-world data on variable selection and causal discovery are also presented to demonstrate the usage of this package. The examples on variable selection and causal discovery show the strong ability of copent on testing (conditional) independence compared with the related packages. The copent package is available on the Comprehensive R Archive Network (CRAN) and also on GitHub at https://github.com/majianthu/copent.