  Interference, which refers to the phenomenon associated with the
superposition of waves, has played a crucial role in the advancement of physics
and finds a wide range of applications in physical and engineering
measurements. Interferometers are experimental setups designed to observe and
manipulate interference. With the development of technology, many quantum
interferometers have been discovered and have become cornerstone tools in the
field of quantum physics. Quantum interferometers not only explore the nature
of the quantum world but also have extensive applications in quantum
information technology, such as quantum communication, quantum computing, and
quantum measurement. In this review, we analyze and summarize three typical
quantum interferometers: the Hong-Ou-Mandel (HOM) interferometer, the N00N
state interferometer, and the Franson interferometer. We focus on the
principles and applications of these three interferometers. In the principles
section, we present the theoretical models for these interferometers, including
single-mode theory and multi-mode theory. In the applications section, we
review the applications of these interferometers in quantum communication,
computation, and measurement. We hope that this review article will promote the
development of quantum interference in both fundamental science and practical
engineering applications.
