A Josephson parametric oscillator (JPO) is an interesting system from the viewpoint of quantum optics because it has two stable self-oscillating states and can deterministically generate quantum cat states. A theoretical proposal has been made to operate a network of multiple JPOs as a quantum annealer, which can solve adiabatically combinatorial optimization problems at high speed. Proof-of-concept experiments have been actively conducted for application to quantum computations. This article provides a review of the mechanism of JPOs and their application as a quantum annealer.