  Applications such as simulating large quantum systems or solving large-scale
linear algebra problems are immensely challenging for classical computers due
their extremely high computational cost. Quantum computers promise to unlock
these applications, although fault-tolerant quantum computers will likely not
be available for several years. Currently available quantum devices have
serious constraints, including limited qubit numbers and noise processes that
limit circuit depth. Variational Quantum Algorithms (VQAs), which employ a
classical optimizer to train a parametrized quantum circuit, have emerged as a
leading strategy to address these constraints. VQAs have now been proposed for
essentially all applications that researchers have envisioned for quantum
computers, and they appear to the best hope for obtaining quantum advantage.
Nevertheless, challenges remain including the trainability, accuracy, and
efficiency of VQAs. In this review article we present an overview of the field
of VQAs. Furthermore, we discuss strategies to overcome their challenges as
well as the exciting prospects for using them as a means to obtain quantum
advantage.
