An extensive series of tetranuclear CuII2LnIII2 complexes [CuIILLnIII(hfac)2]2 (with LnIII being all lanthanide(III) ions except for the radioactive PmIII) has been prepared in order to investigate the nature of the CuII-LnIII magnetic interactions and to try to answer the following question: What makes the CuII2TbIII2 and CuII2DyIII2 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 CuII and LnIII ions are arrayed alternately via bridges of ligand complex (CuIIL). 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 CuII2LnIII2 and NiII2LnIII2 complexes, with the NiII2LnIII2 complex containing diamagnetic NiII ions being used as a reference for the evaluation of the CuII-LnIII magnetic interactions. These measurements have revealed that the interactions between CuII and LnIII 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 CuII2TbIII2, CuII2DyIII2, and NiII2TbIII2 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 CuII2TbIII2 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.