Anomalous ion heating is frequently observed to accompany magnetic reconnection, yet there is little consensus on its origin. Instead of the usual velocity-space analysis, we use phase-space analysis to exhaustively explain how ions are nonthermally energized during collisionless, antiparallel magnetic reconnection. There are both ordered and disordered aspects in the process; the former is explained in terms of conservative quantities, and the latter is explained by demonstrating chaos through a direct calculation of Lyapunov exponents. The former induces “multibeam-like heating” in all three directions, whereas the latter induces stochastic bulk heating. Profiles of the ion temperature tensor components during reconnection can be easily understood by the phase-space distributions of ions in different motional stages.