Recently, \textit{P. Sarkoci} [Aequationes Math. 75, No. 3, 201--207 (2008; Zbl 1148.26016)] has shown that the dominance relation is not transitive in the class of continuous t-norms. When applying triangular norms, mostly some special families are considered and then it is important to know whether the transitivity of the dominance relation holds in such a family. This paper is devoted to the study of several families of continuous Archimedean t-norms (and of Archmedean copulas, which are just 1-Lipschitz Archimedean t-norms). After a comprehensive overview of recent conditions and properties of dominance in general, and in particular cases of some families, five new families of continuous Archimedean t-norms and Archimedean copulas are completely described with respect to the dominance transitivity.