The R package cort implements object-oriented classes and methods to estimate, simulate and visualize certain types of non-parametric copulas. The classic empirical checkerboard copula, and the empirical chekerboard copula with known multivariate margins are avalailables. The core of the package is the Cort algorithm, for Copula Recursive Trees. This algorithm performs a recursive local splitting of the unit hypercube, much like the CART regression algorithm, to fit a piecewise constant copula density. We also provide an efficient way of mixing copulas, allowing to bag the previous algorithms into forests. The algorithms implemented in this package and the corresponding implementation choices will be developped.