  This paper presents a selective survey of recent developments in statistical
inference and multiple testing for high-dimensional regression models,
including linear and logistic regression. We examine the construction of
confidence intervals and hypothesis tests for various low-dimensional
objectives such as regression coefficients and linear and quadratic
functionals. The key technique is to generate debiased and desparsified
estimators for the targeted low-dimensional objectives and estimate their
uncertainty. In addition to covering the motivations for and intuitions behind
these statistical methods, we also discuss their optimality and adaptivity in
the context of high-dimensional inference. In addition, we review the recent
development of statistical inference based on multiple regression models and
the advancement of large-scale multiple testing for high-dimensional
regression. The R package SIHR has implemented some of the high-dimensional
inference methods discussed in this paper.
