Recently several examples of Single Molecule Magnets (SMMs) and Single Chain Magnets (SCMs) containing metal ions with unquenched orbital angular momenta have been reported. The conventional theoretical approaches fail to explain the formation of the magnetization reversal barrier in such molecules. In this contribution we present more comprehensive models of SMMs and SCMs, which properly take into account the orbital effects. First we examine the cyano-bridged trigonal bipyramidal cluster [MnIII(CN)6]2[Mn II (tmphen)2]3 exhibiting SMM properties. The developed model takes into account the spin-orbit interaction and the trigonal crystal field acting on the 3 T1 term of each Mn(III) ion as well as the isotropic exchange interaction between Mn(III) and Mn(II) ions. This model explains both the existence of the barrier and the observed magnetic data. Then we discuss the origin of SMM behavior of the [MnCl]4[Re(triphos)(CN)3]4 molecular cube slightly compressed along one of the C3 axes. We have demonstrated that the magnetic exchange between Re and Mn ions can be approximately described by the Ising-like pseudo-spin-1/2 Hamiltonian. This pseudo-spin-1/2 formalism is applied to the explanation of the magnetic behavior of the Re(II)4Mn(II)4 cube and to the elucidation of the conditions favoring the existence of the barrier. Finally, the SCM behavior of the Co(II) disphosphonate compound Co(H2L)(H2O) with antiferromagnetic exchange is discussed. We show that two factors are responsible for SCM behavior of this compound, namely, the strong singleion anisotropy of the Co(II) ion, and the spin-canting arising from the different orientations of the principal axes of g-tensors for neighboring Co(II) ions. The latter gives rise to an uncompensated magnetic moment along the chain in spite of the fact that the exchange coupling between Co(II) ions is antiferromagnetic. Financial support of the Supreme Council for Science and Technical Development of Moldova is highly appreciated.