Cold atoms and ions provide one of the best ways to build controllable quantum many-body systems as quantum computers and quantum simulators. Here we report on recent developments in programming quantum simulators with focus on hybrid classical-quantum scenarios. Our discussion starts with a brief description of self-verifying variational quantum simulations with trapped ions, illustrated by computing the ground state and quantum phase transition of a lattice Schwinger Model. Furthermore, we report ongoing work in developing measurement protocols to characterize and quantify entanglement in quantum simulators, including efficient learning of `Entanglement Hamiltonians'. This opens interesting perspectives for quantum simulators as a testbed in relation to predictions of Conformal Field Theory, or the Bisognano-Wichmann Theorem of Quantum Field Theory.