The entanglement spectrum, is essential to characterize various phases in condensed matter physics (such as Fractional Quantum Hall effect or Haldane phase). In this talk, I will show how to measure the entanglement spectrum of ground states of generic Hamiltonians based on direct engineering of the entanglement Hamiltonian. Our method, based on the Bisognano-Wichmann theorem, allows to measure entanglement spectra via standard spectroscopy and can be implemented in all quantum simulation platforms. I will provide numerical examples to support this result and give examples of AMO implementations of entanglement Hamiltonians. As an outlook, I will present a method to measure Renyi entropies based on Random Matrix Theory.