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We describe a completely general and fully non-perturbative framework for constructing dynamical reference frames in generally covariant theories, and for understanding the gauge-invariant observables that they yield. Our approach makes use of a 'universal dressing space', which contains as a subset every possible dynamical frame. We describe examples of such frames, including matter frames, a popular construction based on boundary-anchored geodesics and one using minimal surfaces -- but our formalism does not depend on the existence of a boundary. The class of observables we construct generalises and unifies the dressed and relational approaches to constructing gravitational observables, including single-integral and canonical power-series constructions. All these (possibly gravitationally charged) relational observables describe physics in a precise sense relative to the dynamical frame and respect a notion of 'relational' locality based on the relationships between fields. By using 'relational atlases', i.e. collections of dynamical frames glued together by field-dependent maps (which are relational observables too), we can construct relationally local observables throughout spacetime. This further establishes a framework for dynamical frame covariance that permits us to change between arbitrary relational frame perspectives. Relational locality obeys many desirable properties: we prove that it satisfies microcausality in the bulk (in tension with previous work done mainly in a perturbative setting which we comment on), and show that it permits a relational version of local bulk dynamics. Relational locality is therefore arguably more physically meaningful than the ordinary notion of locality. Thus, our formalism -- which we argue to be an updated, gauge-invariant version of general covariance -- refutes the commonly claimed non-existence of local gravitational bulk physics.