This survey contains the main results in rational homotopy, from the beginning to the most recent ones. It makes the status of the art, gives a short presentation of some areas where rational homotopy has been used, and contains a lot of important open problems
Félix, Y., & Halperin, S. (2017). Rational Homotopy Theory via Sullivan Models: A Survey. I C C M Notices, 5(2), 14-36. https://doi.org/10.4310/iccm.2017.v5.n2.a3 (Original work published 2017)