Quantile regression is a powerful and flexible technique that is widely used by econometricians and other applied statisticians. In modern terms we tend to date it back to the classic paper by Koenker and Bassett (1978).
Recently, I reviewed the Handbook of Quantile Regression. This edited volume comprises a number of important, original, contributions to the quantile regression literature. The various chapters cover a wide range of topics that extend the basic quantile regression set-up.
You can read my review of this book (Giles, 2018), here. I hope that it motivates you to explore this topic further.
Giles, D. E., 2018. Review of Handbook of Quantile Regression. Statistical Papers, 59, 849-850.
Koenker, R., 2005. Quantile Regression. Cambridge University Press, Cambridge.
Koenker, R. and G. W. Bassett, 1978. Regression quantiles. Econometrica, 46, 33-50.
Koenker, R., V. Chernozhukov, H. Huming, & L. Peng (eds.), 2017. Handbook of Quantile Regression. Chapman & Hall/CRC, Boca Raton, FL.