  The recent advent of noisy intermediate-scale quantum devices, especially
near-term quantum computers, has sparked extensive research efforts concerned
with their possible applications. At the forefront of the considered approaches
are variational methods that use parametrized quantum circuits. The classical
and quantum Fisher information are firmly rooted in the field of quantum
sensing and have proven to be versatile tools to study such parametrized
quantum systems. Their utility in the study of other applications of noisy
intermediate-scale quantum devices, however, has only been discovered recently.
Hoping to stimulate more such applications, this article aims to further
popularize classical and quantum Fisher information as useful tools for
near-term applications beyond quantum sensing. We start with a tutorial that
builds an intuitive understanding of classical and quantum Fisher information
and outlines how both quantities can be calculated on near-term devices. We
also elucidate their relationship and how they are influenced by noise
processes. Next, we give an overview of the core results of the quantum sensing
literature and proceed to a comprehensive review of recent applications in
variational quantum algorithms and quantum machine learning.
