We will present our first experiments involving multimode cavity QED, wherein the cavity-mediated atom-atom interaction is dramatically modified compared to that in a single-mode cavity. We demonstrate the engineering of strong, tunable-range, and sign-changing photon-mediated interactions between atoms and between atomic spins. A mechanism for photon-mediated interactions based on the Gouy phases of the cavity modes is introduced and demonstrated. Such interactions can be exploited for the creation of unusual quantum many-body phases. Other results include the observation of a ‘spinor density-wave polariton’ condensate and cavity-assisted dynamical spin-orbit coupling. Together, these results pave the way for future experimental access to nontrivial quantum phases and transitions in driven-dissipative quantum systems, synthetic dynamical gauge fields, and the ability to study nonequilibrium spin glasses and quantum neural networks.