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This paper is written for a Festschrift in honour of Professor Marc Hallinand it proposes some developments on quantile regression. We connect ourinvestigation to Marc's scientific production and we present some theoreticaland methodological advances for quantiles estimation in non standard settings.We split our contributions in two parts. The first part is about conditionalquantiles estimation for nonstationary time series. The second part is aboutconditional quantiles estimation for the analysis of multivariate independentdata in the presence of possibly large dimensional covariates. Monte Carlostudies illustrate numerically the performance of our methods and compare themto some extant techniques.

Some novel aspects of quantile regression: local stationarity, random forests and optimal transportation