  The relative entropy and chi-squared divergence are fundamental divergence
measures in information theory and statistics. This paper is focused on a study
of integral relations between the two divergences, the implications of these
relations, their information-theoretic applications, and some generalizations
pertaining to the rich class of $f$-divergences. Applications that are studied
in this paper refer to lossless compression, the method of types and large
deviations, strong~data-processing inequalities, bounds on contraction
coefficients and maximal correlation, and the convergence rate to stationarity
of a type of discrete-time Markov chains.
