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Episode 148 40 years ago, Richard Feynman outlined his vision of a quantum computer for quantum simulations of complex calculations of physical problems. Today, his dream of analog and digital quantum simulations has become a reality and a highly active field of research across different platforms ranging from ultracold atoms and ions, to superconducting qubits and photons. In my talk, I will outline how ultracold atoms in optical lattices started this vibrant and interdisciplinary research field 20 years ago and now allow probing quantum phases in- and out-of-equilibrium with fundamentally new tools and single particle resolution and control. Novel (hidden) order parameters, entanglement properties, full counting statistics or topological features can now be measured routinely and provide deep new insight into the world of correlated quantum matter. I will introduce the measurement and control techniques in these systems and delineate recent applications regarding quantum simulations of strongly correlated electronic systems. IMMANUEL BLOCH is scientific director at the Max Planck Institute of Quantum Optics in Garching and holds a chair for experimental physics at the Ludwig Maximilians University of Munich. His scientific work is among the most frequently cited in the field of quantum physics and has helped to open a new interdisciplinary research field at the interface of atomic physics, quantum optics, quantum information science and solid state physics. For his research, he has received numerous international awards, including the Körber European Science Prize, the Harvey Prize, the Zeiss Research Award and was named Clarivate Citation Laureate in 2022 for his pioneering work on quantum simulations.