This thesis deals with various aspects of the finite model theory of logics with invariantly used relations. To construct such a logic we start with an arbitrary logic L, such as first-order or monadic second-order logic and enrich it by giving it the ability to speak about additional relations such as a linear order which is not actually defined on the structure in question, provided that its truth value be independent of which particular linear order we choose. We investigate how the expressive power of the resulting logics relates to that of the base logic L, and give efficient algorithms for model-checking.