I will present recent developments in the study of quantum many-body phenomena using Rydberg atom arrays, which provide precise and coherent control of hundreds of atoms in two dimensions, along with individual addressability and reconfigurable geometry. First, I will describe explorations of ordering dynamics in a quantum magnet following a quantum phase transition. Using individual atom control, we reveal the interplay of quantum criticality and non-equilibrium dynamics, and observe long-lived oscillations of the order parameter akin to an amplitude (“Higgs”) mode, offering a unique window into the quantum phase transition. I will then describe the digital realization of the Kitaev honeycomb model, including observation of topologically ordered phases, as well as the use of topological order to design a programmable fermionic simulator. Together, these results open new avenues for studying quantum criticality and fermionic systems, highlighting the versatility of atom-based quantum simulators for addressing challenging fundamental questions in quantum science.