The science of dreaming constitutes a relevant topic in modern-day neuroscientific research and provides major insights into the study of human consciousness. Linking specific, universal, and regularly occurring stages of sleep with dreaming encourages the direct and systematic investigation of a topic that has fascinated humankind for centuries. In this review, we explore to what extent individuals dream during periods of rapid eye movement and non-rapid eye movement sleep, and we introduce research on lucid dreaming. We then discuss how dreaming during different stages of sleep varies in terms of phenomenological characteristics, and to what extent individuals are conscious throughout the sleep cycle. Finally, we provide a synopsis of the previous literature on brain activity during sleep, and we aim to clarify how the neurofunctional changes observed throughout sleep may lead to changes in phenomenological aspects of dreams, and in the domain of consciousness.