The project described in this thesis is motivated by a particular interest in Molecular Magnetism from a theoretical point of view. Molecular Magnetism, is still a thriving research field where some problems remain unexplored: A large amount of molecular systems are still theoretically unmanageable due to their huge computational requirements, while the standard software package cannot profit from the power of multiprocessor supercomputers. The scientific community would require a computational code to calculate the magnetic properties of mixed-valence clusters. A new magnetic POM, which needs only one magnetic ion to behave as SMMs, has appeared. A rationalization of its behaviour and an extense study of other candidates is imperative. Considering molecular spintronics, the effect of an external electric field over magnetic molecules should be studied. This thesis is divided in three main chapters. On each one, the author will describe the state-of-the-art before the start of this PhD, the most relevant results obtained and a detailed explanation about his specific contributions. The first chapter, “Computational approaches for Molecular Magnetism”, introduces the author’s contribution to two tools developed for the theoretical understanding of magnetic clusters: The “Parallel implementation of the MAGPACK package for the analysis of high-nuclearity spin clusters” and “MVPACK: A Package to Calculate Energy Levels and Magnetic Properties of High Nuclearity Mixed Valence Clusters”. For the first work the author coordinated a collaboration with the DSIC centre in the Polytechnic University of Valencia. The second code was being written when the author started his PhD, and his contribution was focused in programming the effect of the electric field over mixed-valence systems. The second chapter “Lanthanide Polyoxometalates as Single Ion Magnets” deals with this family of SIMs, which was the second one after Ishikawa’s molecules and the one that effectively opened the field to the current variety of ligand types and structures. The author presents in this chapter three relevant contributions. The first publication is “Mononuclear Lanthanide Single Molecule Magnets Based on the Polyoxometalates [Ln(W5O18)2]9- and [Ln(β2-SiW11O39)2]13- (LnIII = Tb, Dy, Ho, Er, Tm and Yb)” where the initial two series of compounds are synthesized, characterized and theoretically studied. The next is “Lanthanoid Single-Ion Magnets Based on Polyoxometalates with a 5-fold Symmetry: The Series [LnP5W30O110]12- (LnIII = Tb, Dy, Ho, Er, Tm and Yb)” where a lanthanoid complex with a exotic fivefold coordination was completely studied. This is relevant because originally it was thought that only square antiprismatic structures with 4-fold symmetry D4d could be SIMs, and in fact it constituted the motivation for the last paper in this chapter “Rational Design of Single-Ion Magnets and Spin Qubits Based on Mononuclear Lanthanoid Complexes”. There, a theoretical approach based on a point charge model is developed, and suggestions are given for the rational design of both SIMs and spin qubits. The third chapter, “Electric field effects over mixed-valence molecules” presents the application of MVPack to explore the possibilities of an electric control of the magnetic ground state of these molecules. Here, the full contribution “Electrically switchable magnetic molecules: Inducing a magnetic coupling by means of an external electric field in a polyoxovanadate cluster” is introduced.