Delamination problems. ~~~~~~~~~~~~~~~~~~~~ Contact problems of elastic solids with activated, rate-independent delamination on the contact boundary (also called debonding or adhesive contacts) will be addressed. Models at large or small strains will be presented first in a quasistatic formulation based on the concept of energetic solutions. In particular, a brittle delamination model of the Griffith type is exposed and shown to be a limit of a delamination with elastically responding glue that can be thus understood as a regularization which is also suitable to numerical implementation. Further extension to dynamical contact problems in visco-elastic solids and its possible thermodynamics will be briefly outlined, too. The talk will include also results from joint works with M.Kocvara, A.Mielke, L.Scardia, and C.Zanini.