Near-death experiences (NDE) raise important questions about the nature of human consciousness, the relationship between brain function and consciousness, the perceptual information that is available to consciousness in moments before death, the role of physical and biological mechanisms associated with altered states of consciousness, and relationships between consciousness, space-time and phenomenal reality. Challenges posed by efforts to define the NDE, claims of anomalous experiences associated with NDEs, the problem of “timing” of NDEs with respect to brain function, recent findings from neuroscience are reviewed, along with emerging evidence for quantum models of consciousness that may help elucidate the nature of NDEs. I propose that the diversity, complexity and quality of imagery retrospectively interpreted as NDEs reflect a multiplicity of potential neural pathways and the degree to which a heritable NDE predisposition is present in each unique individual. Certain NDE features are probably explainable by neuroscience and take place in 4-dimensional space-time while other NDE features such as confirmed cases of veridical perception and other so-called “anomalous” experiences may be consistent with postulated non-local characteristics of consciousness mediated by quantum-like processes or other non-classical processes (Kafatos et al., 2015) or may reflect relationships between consciousness and the environment that take place in higher order space-times. I propose an integral model that reconciles conventional neural explanations and postulated non-classical models of consciousness. The article concludes with suggestions for animal and human studies aimed at further elucidating neurophysiological mechanisms and postulated quantum-like or other non-classical mechanisms in NDEs and other kinds of transpersonal or so-called “anomalous” experiences. Well-funded cooperative research initiatives in functional brain imaging are leading to rapid advances that will make it possible in the near future to empirically test the integral model put forward in this chapter yielding more complete understandings of consciousness including NDEs and other kinds of transpersonal or anomalous experiences.