The study of consciousness is considered by many one of the most difficult contemporary scientific endeavors and confronts several methodological and theoretical challenges. A central issue that makes the study of consciousness so challenging is that, while the rest of science is concerned with problems that can be verified from a “third person” view (i.e., objectively), the study of consciousness deals with the phenomenon of subjective experience, only accessible from a “first person” view. In the present article, we review early (starting during the late 19th century) and later efforts on measuring consciousness and its absence, focusing on the two main approaches used by researchers within the field: objective (i.e., performance based) and subjective (i.e., report based) measures of awareness. In addition, we compare the advantages and disadvantages of both types of awareness measures, evaluate them according to different methodological considerations, and discuss, among other issues, the possibility of comparing them by transforming them to a common sensitivity measure (d′). Finally, we explore several new approaches—such as Bayesian models to support the absence of awareness or new machine‐learning based decoding models—as well as future challenges—such as measuring the qualia, the qualitative contents of awareness—in consciousness research.