Quantum simulation provides a powerful route to exploring complex many-body systems beyond classical computation. A key frontier is the realization of lattice gauge theories (LGTs), which underpin much of modern physics - from high-energy theory to condensed matter and cosmology. Implementing LGTs with neutral atoms in optical lattices promises to greatly expand the reach of analog quantum simulation and to bridge diverse areas of research. However, local gauge symmetries do not naturally emerge in cold-atom systems and must be engineered. Moreover, the infinite-dimensional Hilbert space of gauge links poses additional challenges. Quantum link models (QLMs), which replace continuous gauge fields by finite-dimensional spin operators, offer a practical path toward experimental implementations. I will provide an overview of recent experimental advances with a focus on results obtained with neutral atoms in optical lattices.
