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[en] This paper describes the conceptual steps in reaching the design of the AWAKE experiment currently under construction at CERN. We start with an introduction to plasma wakefield acceleration and the motivation for using proton drivers. We then describe the self-modulation instability – a key to an early realization of the concept. This is then followed by the historical development of the experimental design, where the critical issues that arose and their solutions are described. We conclude with the design of the experiment as it is being realized at CERN and some words on the future outlook. A summary of the AWAKE design and construction status as presented in this conference is given in Gschwendtner et al. . - Highlights: • Proton-driven plasma wakefield acceleration is proposed to bring electron bunches to high energies. • The self-modulation instability allows the use of existing proton bunches. • Schemes for overcoming the varying wake phase velocity were developed. • AWAKE will demonstrate proton-driven plasma wakefield acceleration for the first time.