The reactivity of solids focuses on time-dependent modifications. The surface of catalysts also undergoes time-dependent modifications during the catalytic cycle. The objective of this contribution is to highlight scientific problems of common interest in the science of solid-state reactivity and in catalysis, especially when the mobility of small chemical species (hydrogen, oxygen) on surfaces, or 'spillover', is involved. This will be illustrated by surface reactions at MoS2 edges and reconstruction of surfaces on MoO3.