We motivate the use of rectangular arrays of Rydberg atoms as analog simulators for Abelian lattice gauge theories. We discuss the rich  phase diagram of the simulator and the continuum limits that can be approached by varying the lattice spacing and the detuning. We compare the cost of estimating  the entanglement entropy with twin copies and bitstring mutual information.  We report recent progress regarding the use of qutrits for simulating the same models. We briefly  discuss hybrid simulations that could be performed in this context.