  In this paper we develop an operational formulation of General Relativity
similar in spirit to existing operational formulations of Quantum Theory. To do
this we introduce an operational space (or op-space) built out of scalar
fields. A point in op-space corresponds to some nominated set of scalar fields
taking some given values in coincidence. We assert that op-space is the space
in which we observe the world. We introduce also a notion of agency (this
corresponds to the ability to set knob settings just like in Operational
Quantum Theory). The effects of agents' actions should only be felt to the
future so we introduce also a time direction field. Agency and time direction
can be understood as effective notions. We show how to formulate General
Relativity as a possibilistic theory and as a probabilistic theory. In the
possibilistic case we provide a compositional framework for calculating whether
some operationally described situation is possible or not. In the probabilistic
version we introduce probabilities and provide a compositional framework for
calculating the probability of some operationally described situation. Finally
we look at the quantum case. We review the operator tensor formulation of
Quantum Theory and use it to set up an approach to Quantum Field Theory that is
both operational and compositional. Then we consider strategies for solving the
problem of Quantum Gravity. By referring only to operational quantities we are
able to provide formulations for the possibilistic, probabilistic, and (the
nascent) quantum cases that are manifestly invariant under diffeomorphisms.
