Many proposals have been made recently for goodness-of-fit testing of copula models. After reviewing them briefly, the authors concentrate on omnibus procedures, i.e., those whose implementation requires neither an arbitrary categorization of the data nor any strategic choice of smoothing parameter, weight function, kernel, window, etc. The authors present a critical review of these omnibus tests and suggest new ones. They describe and interpret the results of a large Monte Carlo experiment designed to assess the effect of the sample size and the strength of dependence on the level and power of the omnibus tests for various combinations of copula models under the null hypothesis and the alternative. To circumvent problems with inaccurate asymptotic approximation of the tests’ limiting null distributions, they recommend the use of a double parametric bootstrap procedure, whose implementation is detailed. They conclude with a number of practical recommendations.