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The ultra-luminous infrared galaxy Arp2 20 is a late-stage merger with several tidal structures in the outskirts and two very compact, dusty nuclei that show evidence for extreme star formation and host at least one AGN. New and archival high-resolution images taken by the Hubble Space Telescope provide a state-of-the-art view of the structures, dust, and stellar clusters in Arp 220. We find that ~90% of the Halpha emission arises from a shock-ionized bubble emanating from the AGN in the western nucleus, while the nuclear disks dominate the Pbeta emission. Four very young (~3-6 Myr) but lower mass (< 10^4 Msun) clusters are detected in Halpha within a few arcsec of the nuclei, but produce less than 1% of the line emission. We see little evidence for a population of massive clusters younger than 100Myr anywhere in Arp 220. From the masses and ages of the detected clusters, we find that star formation took place more-or-less continuously starting ~few Gyr ago with a rate between ~3-12 Msun/yr. Approximately 100Myr ago, star formation shut off suddenly everywhere, except in the nuclear disks. A very recent flicker of weak star formation produced the four young, low-mass clusters, while the rest of the galaxy appears to have remained in a post-starburst state. Cluster ages indicate that the tidal structures on the west side of the galaxy are older than those on the east side, but all appear to pre-date the shutoff of star formation. Arp 220 has many of the characteristics expected of a 'Shocked Post-Starburst Galaxy' or SPOG, since most of the system has been in a post-starburst state for the past ~100Myr and the detected Halpha emission arises from shocked rather than photo-ionized gas., Comment: accepted for publication in the Astrophysical Journal