Deformable models are a powerful tool in both computer graphics and computer vision. The description and implementation of the deformations have to be simultaneously flexible and powerful, otherwise the technique may not satisfy the requirements of all the distinct applications. In this paper, we introduce a new method for the deformable model specification: deformable fields. Deformable fields are conceptually simple, lead to an easy implementation, and are suitable for adaptive models. We apply our new technique to describe an adaptive deformable face, and compare three different adaptation strategies. We show how our technique is suitable to describe different individuals, how to construct a model based on information from a single image, and how it allows the tracking of the deformation parameters over a video sequence.