The reliability function, introduced by Shannon in information theory, is a large-deviation rate function which characterizes the exact exponent under which the error probability of an information processing task approaches zero exponentially. There was little complete result about the reliability function in quantum information. In this talk, I will introduce part of the history and background of this problem, and then I will report our quite recent results on the reliability functions of two quantum information tasks: 1) quantum privacy amplification, and 2) quantum information decoupling. The results are given in terms of a type of information divergence---the Sandwiched Rényi Information Divergence.