String theory, when compactified on a torus, exhibits large duality symmetries, which can be understood in terms of non-perturbative states, for example winding strings and branes. In recent years, a class of models have been developed that are based on the duality symmetries, and in a sense exhibit the symmetry even without compactification. I will give a basic introduction both to the dualities and to the extended geometry models, that are natural generalisations of Einstein gravity.