The catalytic ignition and gas-phase ignition of H-2 in air over platinum are studied in a stagnation-point flow geometry using various gas-phase reaction mechanisms, surface reaction mechanisms, and transport models. Systematically reduced models are developed using a new methodology based on reaction path analysis at turning points along two-parameter bifurcation diagrams. The different reduced models, including algebraic ignition criteria, quantitatively reproduce the catalytic and gas-phase ignition temperatures of the full, spatially distributed model governed by a few thousand equations. Caution is needed in applying reduced mechanisms developed for homogeneous combustion to catalytic combustion. For example, it is found that a reduced gas-phase reaction mechanism, derived for homogeneous combustion alone, must be augmented by H2O2 chemistry for the homogeneous-heterogeneous problem. It is also shown that the rate-limiting surface-reaction step changes with conditions, and common assumptions used in catalysis of fast adsorption-desorption steps of reactants (partial equilibrium) break down under many conditions. Various lumped one-step surface reaction rates are derived to model catalytic combustion of H-2/air mixtures over platinum surfaces. Finally, our analysis shows that under sufficiently fuel-lean conditions, platinum behaves as a source of adsorbed OH species promoting gas-phase ignition. Desorption of adsorbed OH needs then to be included for accurate model predictions.