The distance covariance function is a new measure of dependence between random vectors. We drop the assumption of iid data to introduce distance covariance for time series. The R package dCovTS provides functions that compute and plot distance covariance and correlation functions for both univariate and multivariate time series. Additionally it includes functions for testing serial independence based on distance covariance. This paper describes the theoretical background of distance covariance methodology in time series and discusses in detail the implementation of these methods with the R package dCovTS.