Potential density of integral points and Campana's theory of special varieties and C-pairs

Which varieties over a number field should have a potentially dense set of integral points? We provide evidence for Campana's conjecture that this should be the class of (Campana-)special varieties; these are varieties which are as far away as possible from being of (log-)general type and includes algebraic groups, Calabi-Yau varieties and rationally connected varieties. Joint with Finn Bartsch, Frederic Campana, and Olivier Wittenberg.