I will present some of the fundamental aspects of classical realizability. Firstly, we will have a brief look into the history and motivation behind the study of realizability, starting from the Brouwer–Heyting–Kolmogorov interpretation of intuitionistic logic and Kleene’s original number realizability. Afterwards we will examine how these ideas can be adapted to classical logic by exploring the mechanisms behind Krivine’s classical realizability. This talk is the result of a reading course in the Master of Logic programme.