Let \((M^{2m}, g)\) be a submanifold of a quaternionic Kähler manifold \((\widetilde{M}^{4n},Q,\widetilde{g})\) with induced metric \(g=\widetilde{g}_{|M}\) and \(J\) a \(g\)-orthogonal almost complex structure on \(M^{2m}\). The manifold \((M^{2m},J,g)\) is called an almost Hermitian submanifold of \(\widetilde{M}\) if there is a section \(J_1:M \rightarrow Q_{|M}\) such that \(J_1 T_xM=T_x M\), for all \(x\in M\) and \(J=J_{1{|TM}}\). In this paper the authors study the properties of almost Hermitian submanifolds of different types (Hermitian, almost Kähler, Kähler,\dots) of a quaternionic Kähler manifold. Thus, in section 1 they give conditions for an almost Hermitian submanifold to be Hermitian, and prove that any almost Kähler submanifold is Kähler and, hence, a minimal submanifold and give some local characterizations of such submanifold. In section 2 they study Kähler submanifolds of quaternionic Kähler manifolds, locally symmetric quaternionic Kähler manifolds, or quaternionic space forms. In Section 3 the authors give a classification of Kähler submanifolds of quaternionic Kähler manifolds with parallel non zero second fundamental form (i.e., parallel Kähler submanifolds). Finally, in section 4 the authors prove some result on non existence of non totally geodesic curvature invariant Kähler submanifold on a locally symmetric quaternionic Kähler manifold.