Meditation has been integral to human culture for millennia, deeply rooted in various spiritual and contemplative traditions. While the field of contemplative science has made significant steps toward understanding the effects of meditation on health and well-being, there has been little study of advanced meditative states, including those achieved through intense concentration and absorption. We refer to these types of states as advanced concentrative absorption meditation (ACAM), characterized by absorption with the meditation object leading to states of heightened attention, clarity, energy, effortlessness, and bliss. This review focuses on a type of ACAM known as jhana (ACAM-J) due to its well-documented history, systematic practice approach, recurring phenomenological themes, and growing popularity among contemplative scientists and more generally in media and society. ACAM-J encompasses eight layers of deep concentration, awareness, and internal experiences. Here, we describe the phenomenology of ACAM-J and present evidence from phenomenological and neuroscientific studies that highlight their potential applications in contemplative practices, psychological sciences, and therapeutics. We additionally propose theoretical ACAM-J frameworks grounded in current cognitive neuroscientific understanding of meditation and ancient contemplative traditions. We aim to stimulate further research on ACAM more broadly, encompassing advanced meditation including meditative development and meditative endpoints. Studying advanced meditation including ACAM, and specific practices such as ACAM-J, can potentially revolutionize our understanding of consciousness and applications for mental health.