The AWAKE Collaboration is pursuing a demonstration of proton-driven plasma wakefield acceleration of electrons. The AWAKE experiment uses a 400GeV/c proton bunch from the CERN SPS, with a rms bunch length of 6-15 cm, to drive wakefields in a 10 m long rubidium plasma with an electron density of 1014 — 1015cm−3. Since the drive bunch length is much longer than the plasma wavelength (λpe <3 mm) for these plasma densities, AWAKE performed experiments to prove that the long proton bunch self-modulates in the plasma (2017). The next step is to demonstrate acceleration of electrons in the wakefields driven by the self-modulated bunch (2018). We summarize the concept of the self-modulation measurements and describe the plans and challenges for the electron acceleration experiments.