  This paper gives a review of concentration inequalities which are widely
employed in non-asymptotical analyses of mathematical statistics in a wide
range of settings, from distribution-free to distribution-dependent, from
sub-Gaussian to sub-exponential, sub-Gamma, and sub-Weibull random variables,
and from the mean to the maximum concentration. This review provides results in
these settings with some fresh new results. Given the increasing popularity of
high-dimensional data and inference, results in the context of high-dimensional
linear and Poisson regressions are also provided. We aim to illustrate the
concentration inequalities with known constants and to improve existing bounds
with sharper constants.
