This work presents a survey of computational methods for adhesive contact focusing on general continuum mechanical models for attractive interactions between solids that are suitable for describing bonding and debonding of arbitrary bodies. The most general approaches are local models that can be applied irrespective of the geometry of the bodies. Two cases can be distinguished: local material models governing the constitutive behavior of adhesives, and local interface models governing adhesion and cohesion at interfaces in the form of traction-separation laws. For both models various sub-categories are identified and described, and used to organize the available literature that has contributed to their advancement. Due to their popularity and importance, this survey also gives an overview of effective adhesion models that have been formulated to characterize the global behavior of specific adhesion problems.