  Accurate models for open quantum systems -- quantum states that have
non-trivial interactions with their environment -- may aid in the advancement
of a diverse array of fields, including quantum computation, informatics, and
the prediction of static and dynamic molecular properties. In recent years,
quantum algorithms have been leveraged for the computation of open quantum
systems as the predicted quantum advantage of quantum devices over classical
ones may allow previously inaccessible applications. Accomplishing this goal
will require input and expertise from different research perspectives, as well
as the training of a diverse quantum workforce, making a compilation of current
quantum methods for treating open quantum systems both useful and timely. In
this Review, we first provide a succinct summary of the fundamental theory of
open quantum systems and then delve into a discussion on recent quantum
algorithms. We conclude with a discussion of pertinent applications,
demonstrating the applicability of this field to realistic chemical,
biological, and material systems.
