  We prove the Ramsey property for classes of ordered structures with closures
and given local properties. This generalises earlier results: the
Ne\v{s}et\v{r}il-R\"odl Theorem, the Ramsey property of partial orders and
metric spaces as well as the authors' Ramsey lift of bowtie-free graphs. We use
this framework to solve several open problems and give new examples of Ramsey
classes. Among others, we find Ramsey lifts of convexly ordered $S$-metric
spaces and prove the Ramsey theorem for finite models (i.e. structures with
both functions and relations) thus providing the ultimate generalisation of the
structural Ramsey theorem. Both of these results are natural, and easy to
state, yet their proofs involve most of the theory developed here.
  We also characterise Ramsey lifts of classes of structures defined by
finitely many forbidden homomorphisms and extend this to special cases of
classes with closures. This has numerous applications. For example, we find
Ramsey lifts of many Cherlin-Shelah-Shi classes.
