Copulas have become a popular tool in multivariate modeling successfully applied in many fields. A good open-source implementation of copulas is much needed for more practitioners to enjoy the joy of copulas. This article presents the design, features, and some implementation details of the R package copula. The package provides a carefully designed and easily extensible platform for multivariate modeling with copulas in R. S4 classes for most frequently used elliptical copulas and Archimedean copulas are implemented, with methods for density/distribution evaluation, random number generation, and graphical display. Fitting copula-based models with maximum likelihood method is provided as template examples. With the classes and methods in the package, the package can be easily extended by user-defined copulas and margins to solve problems.