Organometallic ruthenium(II)-arene (RA) antitumour compounds of the general type [Ru(II)(η6-arene)(X)2(pta)], RA-pta, and [Ru(II)(η6-arene)X(en)], RA-en, (X=leaving group; pta=1,3,5-triaza-7-phosphaadamantane, en=ethylenediamine) have been investigated computationally. The main focus has been i.e. the hydrolysis properties, ligand exchange reactions, binding to DNA and the analysis of the resulting structural perturbations. The goal of this thesis was to elucidate key steps in the reactivity of the above drugs that are not readily accessible by experimental techniques. The methodologies employed cover tailor made force fields in classical molecular dynamics (MD), density functional theory (DFT) MD simulations in implicit and explicit solvent as well as combined classical/quantum (QM/MM) MD simulations. For RA-pta compounds, binding energies between the metal centres and the surrounding ligands were calculated. The calculated energies rationalize the experimentally observed tendencies for arene loss, and show that the pta ligands are relatively strongly bound. Exchange of metal centre, methylation or protonation of the pta-ligand, or change of the arene result in significant differences in the metal-arene binding energies while leaving the metalphosphine bond strength essentially unchanged. Significantly lower binding energies and reduced hapticity are predicted for the exchange of arene by nucleobases. The latter show higher binding energies for nitrogen π-bonding than for p-bonding. No influence on the ruthenium-arene interaction was observed for RA-pta complexes bearing arenes with functionalized side chains. A combined DFT/continuum electrostatics approach has been used to estimate the protonation states and absolute pKa values of a series of RA-pta compounds and their hydrolysis products. Our results suggest that the selective in vivo activity towards cancer cells and the observed pH dependent DNA damage is due to a pH dependent activation/deactivation mechanism. In the context of rational drug design, it is hypothesised that analogues with fluorinated arene rings should result in improved selectivity towards hypoxic cancer cells. For RA-en complexes, we rationalized the chemoselectivity towards guanine. The calculated DFT binding energies for the three investigated nucleobases (G, A, C) decreases in the order G(N7) >> C(O2) ∼ C(N3) > A(N7) > G(O6) > OH2. The G(N7) complex is the most stable product due to a C6=O-HNen hydrogen bond while the corresponding C6-NH2-HNen interaction in adenine is repulsive. A study of the reaction of [(η6-benzene)Ru(en)(OH2)]2+ (1) towards the nucleobases G, A and C reveals a strong preference for a formation of an H-bonded cis vs. trans reactant adduct. Only guanine can form a thermally stable trans reactant adduct. The potential reaction sites of adenine and cytosine might loose their nucleophilicity by protonation while simultaneously the aqua leaving group of 1 is converted into an unreactive hydroxo ligand. For the reaction of 1 with guanine three different reaction pathways were identified, however, a "direct trans" reaction pathway is probably the most biologically relevant. Using classical and QM/MM MD we showed that both investigated ruthenium compounds, RA-pta and RA-en, can bind to the major groove of duplex DNA and are stable in this position. The DNA is highly flexible, adapts very fast and widens the major groove to accommodate the ruthenium complex. The local and global structural changes of the DNA (e.g. bending towards the major groove) observed for the RA-pta series are similar to those reported for cisplatin. A severe perturbation of the Watson-Crick base pairing adjacent to the binding site of RA-en was observed that can be linked to recent experimental results. Finally, a tailor made force field for RA-en was derived from our QM/MM trajectories using a force matching approach.