The physical basis of the catalytic power of enzymes remains contentious despite sustained and intensive research efforts. Knowledge of enzyme catalysis is predominantly descriptive, gained from traditional protein crystallography and solution studies. Our goal is to understand catalysis by developing a complete and quantitative picture of catalytic processes, incorporating dynamic aspects and the role of quantum tunnelling. Embracing ideas that we have spearheaded from our work on quantum mechanical tunnelling effects linked to protein dynamics for H-transfer reactions, we review our recent progress in mapping macroscopic kinetic descriptors to an atomistic understanding of dynamics linked to biological H-tunnelling reactions.