  Operator-valued Schatten spaces were introduced by G. Pisier as a
noncommutative counterpart of vector-valued $\ell_p$-spaces. This family of
operator spaces forms an interpolation scale which makes it a powerful and
convenient tool in a variety of applications. In particular, as the norms
coming from this family naturally appear in the definition of certain entropic
quantities in Quantum Information Theory (QIT), one may apply Pisier's theory
to establish some features of those quantities. Nevertheless, it could be quite
challenging to follow the proofs of the main results of this theory from the
existing literature. In this article, we attempt to fill this gap by presenting
the underlying concepts and ideas of Pisier's theory in a self-contained way
which we hope to be more accessible, especially for the QIT community at large.
Furthermore, we describe some applications of this theory in QIT. In
particular, we prove a new uniform continuity bound for the quantum conditional
R\'enyi entropy.
