In 1968, Heskins and Guillet published the first systematic study of the phase diagram of poly(N-isopropylacrylamide) (PNIPAM), at the time a "young polymer" first synthesized in 1956. Since then, PNIPAM became the leading member of the growing families of thermoresponsive polymers and of stimuli-responsive, "smart" polymers in general. Its thermal response is unanimously attributed to its phase behavior. Yet, in spite of 50 years of research, a coherent quantitative picture remains elusive. In this Review we survey the reported phase diagrams, discuss the differences and comment on theoretical ideas regarding their possible origins. We aim to alert the PNIPAM community to open questions in this reputably mature domain.