The magnetic anisotropy of complexes with strong spin-orbit coupling effects started to be successfully investigated in the recent years by state-of-the-art ab initio methods [1,2]. The blocking of magnetization in these complexes is found to depend crucially on the smallness of transversal Zeeman interaction or intrinsic tunneling gaps on the metal ions, i.e., on their magnetic axiality. The examples include single- and polynuclear Ln complexes, as well as mixed lanthanide - transition metal (TM) compounds. In this presentation, the recent achievements in the theoretical study of blocking of magnetization in strongly anisotropic magnetic complexes will be overviewed. First, complexes involving one single lanthanide ion will be considered, for which the quantum tunneling of magnetization and the activated regime of magnetic relaxation will be discussed. In the second part, polynuclear lanthanide complexes will be described for which the interplay between the anisotropy of individual ions and the exchange interaction between them will be emphasized. Finally, the mixed 4f-3d complexes will be considered for which we will demonstrate the existence of two relaxation regimes, of intra-ionic and of exchange-blocking origin [3,4].