An extensive series of tetranuclear Cu(2)(II)Ln(2)(III) complexes [Cu(II)LLn(III)(hfac)(2)](2) (with Ln(III) being all lanthanide(III) ions except for the radioactive Pm-III) has been prepared in order to investigate the nature of the Cu-II-Ln(III) magnetic interactions and to try to answer the following question: What makes the (Cu2Tb2III)-Tb-II and (Cu2Dy2III)-Dy-II complexes single molecule magnets while the other complexes are not? All the complexes within this series possess a similar cyclic tetranuclear structure, in which the Cu-II and Ln(III) ions are arrayed alternately via bridges of ligand complex ((CuL)-L-II). Regular SQUID magnetometry measurements have been performed on the series. The temperature-dependent magnetic susceptibilities from 2 to 300 K and the field-dependent magnetizations from 0 to 5 T at 2 K have been measured for the Cu(2)(II)Ln(2)(III) and Ni(2)(II)Ln(2)(III) complexes, with the Ni(2)(II)Ln(2)(III) complex containing diamagnetic Ni-II ions being used as a reference for the evaluation of the Cu-II-Ln(III) magnetic interactions. These measurements have revealed that the interactions between Cu-II and Ln(III) ions are very weakly antiferromagnetic if Ln = Ce, Nd, Sm, Yb, ferromagnetic if Ln = Gd, Tb, Dy, Ho, Er, Tm, and negligible if Ln = La, Eu, Pr, Lu. With the same goal of better understanding the evolution of the intramolecular magnetic interactions, X-ray magnetic circular dichroism (XMCD) has also been measured on (Cu2Tb2III)-Tb-II, (Cu2Dy2III)-Dy-II, and (Ni2Tb2III)-Tb-II complexes, either at the L-and M-edges of the metal ions or at the K-edge of the N and O atoms. Last, the (Cu2Tb2III)-Tb-II complex exhibiting SMM behavior has received a closer examination of its low temperature magnetic properties down to 0.1 K. These particular measurements have revealed the unusual very slow setting-up of a 3D order below 0.6 K.