Consciousness is one of the greatest unsolved mysteries of the brain. The simple and yet fundamental question, “How do we have subjective experience?” remains a matter of great debate among neuroscientists. These debates have generated some challenges for consciousness research, namely the hard problem—do normal scientific approaches work for consciousness— and the binding problem—how are sensory inputs experienced in a unified manner? Historically, consciousness has been studied by searching for the neural correlates of consciousness which are defined as the minimal brain areas jointly necessary for conscious experience. One of the most popular experimental paradigms used to investigate the neural correlates of consciousness is binocular rivalry. In binocular rivalry, separate images are simultaneously presented to each eye and perception vacillates between them, providing a way of determining which neural changes are due to shifts in perceptual consciousness rather than changes in stimuli. As the research progressed, however, scientists realized that finding correlates of consciousness was insufficient and that explanatory theories of consciousness were needed to make further progress. This review article aims to introduce the field of consciousness research by presenting some of the core challenges to the field: tracing the search for the neural correlates of consciousness through the lens of binocular rivalry, and exploring four popular theories of consciousness. These are higher-order theory, global neuronal workspace theory, integrated information theory, and predictive processing. It concludes with a glance at the future directions of research that aim to resolve the beguiling phenomenon of consciousness.