We have summarized part of our work involving first principles molecular dynamics simulations on organometallic-based homogeneous catalysts. Explicit dynamics effects can be uniquely extracted from such simulations, and related to structure and reactivity. Examples given deal with metallocene-based ethylene polymerisation, ethylene insertion in a platinum hydride, and olefin metathesis. The dynamics simulations in particular reveal information on the flexibility of these molecular systems, and elucidate mechanistic details (e.g., relevance agostic interaction). For the Ru-based metathesis catalyst an alternative simulation approach has been applied, which has enabled us to make derailed comparison between simulation results and the reaction mechanism proposed by Dias et al. [E.L. Dias, S.T. Nguyen, R.H. Grubbs, J. Am. Chem. Sec. 119 (1997) 3887], showing that the results of our simulations reveal and lend support to the mechanism proposed by Grubbs. These include, in the order of appearance in the reaction scheme, the relative easiness of Cl-Ru-Cl cis-trans configurational exchange, carbene rotation and the loss of one phosphine, formation of a metallacyclobutane intermediate, and finally completion of the metathesis reaction. The presence of a small fraction of the monophosphine complex is confirmed by the present simulations. Starting from the observation that selective bond excitation is necessary to exhibit reactivity, the higher activity of the monophosphine system compared to bisphosphine complexes reported by Dias et al, can be understood.