General anesthesia reversibly alters consciousness, without shutting down the brain globally. Depending on the anesthetic agent and dose, it may produce different consciousness states including a complete absence of subjective experience (unconsciousness), a conscious experience without perception of the environment (disconnected consciousness, like during dreaming), or episodes of oriented consciousness with awareness of the environment (connected consciousness). Each consciousness state may potentially be followed by explicit or implicit memories after the procedure. In this respect, anesthesia can be considered as a proxy to explore consciousness. During the recent years, progress in the exploration of brain function has allowed a better understanding of the neural correlates of consciousness, and of their alterations during anesthesia. Several changes in functional and effective between-region brain connectivity, consciousness network topology, and spatio-temporal dynamics of between-region interactions have been evidenced during anesthesia. Despite a set of effects that are common to many anesthetic agents, it is still uneasy to draw a comprehensive picture of the precise cascades during general anesthesia. Several questions remain unsolved, including the exact identification of the neural substrate of consciousness and its components, the detection of specific consciousness states in unresponsive patients and their associated memory processes, the processing of sensory information during anesthesia, the pharmacodynamic interactions between anesthetic agents, the direction-dependent hysteresis phenomenon during the transitions between consciousness states, the mechanisms of cognitive alterations that follow an anesthetic procedure, the identification of an eventual unitary mechanism of anesthesia-induced alteration of consciousness, the relationship between network effects and the biochemical or sleep-wake cycle targets of anesthetic agents, as well as the vast between-studies variations in dose and administration mode, leading to difficulties in between-studies comparisons. In this narrative review, we draw the picture of the current state of knowledge in anesthesia-induced unconsciousness, from insights gathered on propofol, halogenated vapors, ketamine, dexmedetomidine, benzodiazepines and xenon. We also describe how anesthesia can help understanding consciousness, we develop the above-mentioned unresolved questions, and propose tracks for future research.