Over the last few years, synthetic quantum systems of cold neutral atoms, trapped ions, superconducting qubits, electron spin qubits, etc, have reached a new era: Programmable coherent interactions can be implemented between tens of particles, and in highly tunable geometries. These experimental breakthroughs raise important prospects for quantum simulation, where models that are fundamental for condensed matter or high-energy physics can be experimentally realized. Synthetic quantum systems can be also used to build quantum computers. These devices offer the prospect to outperform classical computers, in particular to solve hard classical optimization problems. I will present protocols for measuring entanglement in such `quantum processors'. The idea of measuring entanglement is first very relevant to benchmark quantum computers, as it demonstrates the most elementary of the quantum properties, independently of the model, assumptions on the state, classical simulations, etc. In the framework of quantum simulation of condensed matter and high-energy physics theories, experimental access to the universal properties of entanglement describing quantum matter in-/(out-of-) equilibrium have also raised significant interest. The talk is outlined as follows: First, I will introduce the concept of entanglement, in relation with quantum computers and quantum simulators. I will then present the randomized measurement toolbox, which gives experimental access to entanglement-related quantities. This will be illustrated with recent experimental works performed on quantum computers and simulators. I will conclude by mentioning recent upgrades/challenges for the toolbox.