Codensity liftings provide a general method for constructing liftings of endofunctors and monads along fibrations. The idea originates from the construction of logical predicates for monadic types introduced by Lindley and Stark. Codensity liftings are connected to a variety of mathematical constructions involving preorders, relations, topologies, and metrics, including the lower and upper preorders on powersets and the Kantorovich metric on probability distributions. In this talk, I will present applications of codensity liftings to the theory of bisimulations for coalgebraic transition systems.