The sperm whale lives in most deep ice-free waters of the globe. It was targeted during two periods of whaling peaking in the 1840’s and 1960’s. Using a habitat suitability model, we extrapolated estimates of abundance from visual and acoustic surveys to give a global estimate of 736,053 sperm whales (CV = 0.218) in 1993. Estimates of trends in the post-whaling era suggest that: whaling, by affecting the sex ratio and/or the social cohesion of females, reduced recovery rates well after whaling ceased; preferentially-targeted adult males show the best evidence of recovery, presumably due to recruitment from breeding populations; several decades post-whaling, sperm whale populations not facing much human impact are recovering slowly, but populations may be declining in areas with substantial anthropogenic footprint. A theta-logistic population model enhanced to simulate spatial structure and the non-removal impacts of whaling indicated a pre-whaling population of 1,949,698 (CV = 0.178) in 1710 being reduced by whaling, and then then recovering a little to about 844,761 (CV = 0.209) in 2022. There is much uncertainty about these numbers and trends. A larger population estimate than produced by a similar analysis in 2002 is principally due to a better assessment of ascertainment bias.