 This paper proposes a methodology for calculating return periods and design quantiles in a multi-dimensional environment. It introduces a consistent theoretical framework for the calculation of return periods using copulas and the Kendall's Tau measure. Additionally, it presents different approaches for identifying suitable design events, which are of utmost importance in practical applications. A case study involving the behavior of a dam is used to illustrate the proposed methods. This article was authored by G. Salvadori, C. de Michele and F. Durante.