Atoms and photons are the fundamental building blocks of our universe. Their interactions rule the behavior of our physical world but at the same time can be extremely complex, especially in the context of many-body quantum systems. Understanding and harnessing them is one of the major challenges of modern quantum science. In recent years, ultracold atomic systems have emerged as a pristine platform for the exploration of atom-light interactions. In this talk, I will discuss the potential of atomic systems loaded in optical cavities as a resource to enhance the energy scales needed to observe complex many-body behaviors by harnessing infinity range interactions mediated by photons that can couple a large set of internal levels. I will show how cavity systems can help us not only to shed light on behaviors of iconic Hamiltonians describing real materials but also to engineer broader classes of Hamiltonians with multi-body interactions too complex to emerge naturally. Furthermore , I will explain how they can facilitate the generation of quantum entanglement and overcome physical constraints currently limiting the performance of state-of-the-art atomic clocks and interferometers.