 Penrose's original formulation relied on black holes: a suitably generic singularity will always be contained in a black hole (and so causally invisible outside the black hole). As the counter-examples to various ways of articulating the hypothesis based on this idea have accumulated over the years, however, it has gradually been abandoned (Geroch and Horowitz 1979; Krolak 1986; Penrose 1998; Joshi et al. 2002; Joshi 2003, 2007a; Joshi and Malafarina 2011a, 2011b). More recent approaches either begin with an attempt to provide necessary and sufficient conditions for cosmic censorship itself, yielding an indirect characterization of a naked singularity as any phenomenon violating those conditions, or else they begin with an attempt to provide a characterization of a naked singularity without reference to black holes and so conclude with a definite statement of cosmic censorship as the absence of such phenomena (Geroch and Horowitz 1979). The variety of proposals made using both approaches is too great to canvass here; the interested reader is referred to Ringström (2010) for a review of the current state of the art for standard black holes, Nielsen (2012) for cosmic censorship regarding Hayward's quasi-local black holes  (section 3.3),  Ringström (2010) for a review of the bearing of the initial-value problem in general relativity on cosmic censorship, and to Earman (1995, ch. 3) and Curiel (1999) for philosophical discussion of many of the earlier proposals. Manchak (2011) gives reasons for thinking that the question of providing a completely satisfactory formulation of the Cosmic Censorship Hypothesis may never be settled, on the grounds that the idea of what counts as “physically reasonable” is not an empirically determinable question. Still, the possibility may remain open that there be several different, inequivalent formulations of the Cosmic Censorship Hypothesis, each having its own advantages and problems, none “canonical” in a definitive sense, as may be the case for definitions of singularities and black holes themselves. 