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Supplementing earlier literature by e.g. Tipler, Clarke, & Ellis (1980),Israel (1987), Thorne, (1994), Earman (1999), Senovilla & Garfinkle (2015),Curiel (2019ab), and Landsman (2021ab), I provide a historical and conceptualanalysis of Penrose's path-breaking 1965 singularity (or incompleteness)theorem. The emphasis is on the nature and historical origin of the assumptionsand definitions used in-or otherwise relevant to-the theorem, as well as on thediscrepancy between the (astro)physical goals of the theorem and its actualcontent: even if its assumptions are met, the theorem fails to prove theexistence or formation of black holes.Penrose himself was well aware of thisgap, which he subsequently tried to overcome with his visionary and influentialcosmic censorship conjectures. Roughly speaking, to infer from (null) geodesicincompleteness that there is a "black" object one needs weak cosmic censorship,whereas in addition a "hole" exists (as opposed to a boundary of an extendiblespace-time causing the incompleteness of geodesics) if strong cosmic censorshipholds.

Penrose's 1965 singularity theorem: From geodesic incompleteness to cosmic censorship