Multi-time quantum processes are endowed with the same richness as many-body physics, including temporal entanglement and well-defined causal structures. We dub this many-time physics, and show how surprisingly accessible, yet under-explored, these phenomena are in nascent quantum processors. Here, we develop a family of tools that allow us access to many-time physics on quantum information processors, which are then demonstrated. First, we access short-range microscopic properties, such as genuine multi-time entanglement and estimators for non-Markovian memory. Then, adapting classical shadow tomography to many-time scenarios, we access macroscopic features like long-range correlations and compact representations of large processes. We showcase this for a 20-step process (42-qubit state) by accurately capturing numerous facets of the dynamics, including multi-time correlations -- for example, in the prediction of mid-circuit measurement distributions. Our techniques are pertinent to generic quantum stochastic dynamical processes, with a scope ranging across condensed matter physics, quantum biology, and in-depth diagnostics of NISQ era quantum devices.