The Many Faces of Interpolation Johan van Benthem Abstract: This is a survey of five unusual takes on what the Interpolation Theorem says, as a form of 'model-crossing inference' involving changing vocabulary, mixed with preservation behaviour. Connections include Bolzano in the history of logic, and computational fixed-point logics. The material was presented at the Berkeley 'Craigfest', May 2007, honouring Bill Craig's 90th birthday, and it will appear in a special issue of "Synthese", edited by Paolo Mancosu.