Claims from those having near-death experiences (NDEs), as well as those sympathetic to such claims, challenge the prevailing assumption that consciousness is dependent on a functioning brain. Extant theories, both neurobiological and psychosocial, that attempt to explain NDEs are examined and found unable to adequately account for the full range of NDE reports, especially electromagnetic after-effects and out-of-body experiences with veridical perception. As a result, many leading NDE researchers have proposed that a new model is needed to explain how consciousness could possibly exist independently of the brain, mainly relying on theories from quantum physics. Our paper critically evaluates a range of extant neurobiological and psychosocial theories of NDEs, as well as examines theories that might offer more promise in fully explaining NDEs, especially those using insights derived from quantum physics. We conclude that the "hard problem" of consciousness is not yet solved, but that NDEs provide an important avenue for exploring the relationship between consciousness and brain, as well as possibly understanding a disembodied concept of consciousness.