Abstract: In model theory certain simple combinatorial structures serve as a device for distinguishing important classes of theories. For example, instability may be defined by interpretation of an infinite linear ordering. Superstability may be defined by means of interpreting certain trees. Certain profinite structures (e.g. profinite groups) appear naturally in model theory, for instance when T is stable and G is a group definable in T, then the group G/G^0 is profinite. We propose a model-theoretic framework for investigating profinite structures, particularly those interpretable in small theories. It turns out, that several results from geometric model theory (like group existence theorems of Hrushovski) have natural counterparts in this new set-up. There are some obvious similarities in the proofs, however the proofs require also some new ideas. They are also accessible to a non-model theorist, although have a strong model-theoretic flavour. Every finite structure is interpretable in any infinite model (with parameters). It is not so with profinite structures. Small profinite structures may serve as a tool for investigating simple theories.