In this thesis, quantum chemical methods were used to study the magnetochemistry of 3d transition metal and lanthanide-based systems. Along this line, ab initio multi-reference methods such as CASSCF as well as CASPT2 and calculations based on density functional theory were used. The focus was on the additional gain of information through the application of different theoretical methods, the development of new approaches as well as suitable structural models, and the verification of analytical models used for the evaluation of experimental data. The theoretically investigated magnetic systems in this thesis are potentially suitable either as single-molecule magnets (chapters 2 and 3), namely as molecular storage units, or for application as molecular electron spin quantum bits in quantum computers (chapter 4). Both research areas are strongly interdisciplinary and combine the fields of chemistry, physics, engineering, and computer science. However, the application of potentially suitable molecules, such as the presented ones, as single-molecule magnets or quantum bits, respectively, is still very limited. Nevertheless, the detailed investigation of properties at the molecular and atomic level by methods of computational chemistry is of great benefit and can help to verify and complement experimental results. Another advantage of computational chemistry is the increase in computing power due to technological progress. As a result, it is possible to apply highly accurate computational methods to systems continuously growing in size. Last but not least, the expanding importance of computational chemistry can be seen from an increasing number of scientific publications which besides experimental work, also contain theoretical contributions based on computational studies. By combining theoretical and experimental results, trends can be found, deduced, and extrapolated which can then be useful for the future design of molecules with desired magnetic properties.