Nanosized metal particles absorb and scatter light through the collective excitations of their free electrons. The excitation of these plasmons gives rise to the bright red color of nanoparticle-stained glass. It also enhances optical processes close to the metal and is exploited for sensing and analytics. A large part of the plasmonenergy is stored in electromagnetic near fields at the metal surface. When two particles are close together, their near fields interact resulting in hybridized collective states. This led to the idea of nanoparticle agglomerates as plasmonic molecules, polymers, and crystals.In my talk, I will present crystals of close-packed plasmonic nanoparticles, where the interparticle distance is much smaller than the particle size. The interaction of light with the crystal plasmons is so strong that the interactionstrength exceeds the plasmon frequency, which is known as deep-strong coupling. The light-matter Hamiltonian becomes dominated by terms that create virtual excitations in the ground state and separate light and matter in frequency and space. We realized such materials by growing face centered cubic supercrystals from gold nanoparticles. Their optical properties reveal Rabi frequencies of several eV. Metallic and semiconducting nanoparticles may work as building blocks for an entire class of materials with extreme light-matter interaction. They will have application in nonlinear optics, the search for cooperative effects and novel ground states, polariton chemistry, and quantum information technology.