Let $G$ be a graph and $\mu (G)$ its Mycielskian graph. Roman and Italian domination, together with their independent and total variants, have been extensively studied, including studies on graph operators and products. In this article, we investigated the behavior of these domination parameters in Mycielskian graphs and, in particular, we provided closed formulas for these invariants in $\mu (G)$ in terms of the corresponding values of $G$.