Sevryuk M.B. Invariant tori of intermediate dimensions in Hamiltonian systems: A brief survey (42K, LaTeX 2.09) ABSTRACT. In the present paper, we survey recent results on the existence and the structure of Cantor families of invariant tori of dimensions $p>n$ in a neighborhood of families of invariant $n$-tori in Hamiltonian systems with $d\geq p$ degrees of freedom.