Specialisations and algebraically closed fields

We study the theory of specialisations in algebraic geometry from a model theoretic viewpoint. In particular we investigate universality and maximality of specialisations on algebraically closed fields, and on algebraic varieties definable in them. We show that specialisations on algebraically closed fields are given by valuations, and the theory of specialisations of algebraically closed fields is a part of the theory of algebraically closed valued fields. In this sense, the theory of specialisations for algebraic varieties definable over algebraically closed fields can be seen as a generalisation of valuations to varieties.