Ruthenium based catalysts remain among the more successful complexes used in the catalysis of metathesis processes for the synthesis of new carbon-carbon bonds. The investigation of the influence of the different system moieties on its catalytic performance has led to important improvements in the field. To this extent, density functional theory (DFT) calculations have contributed significantly providing fundamental understandings to develop new catalysts. With this aim, we presented here a detailed computational study of how the nature of the anion ligand binding to the metal affects the global properties and reactivity of the catalyst. Geometric, energetic and electronic analysis have been performed to reach the key insights necessary to build structure-performance correlations.