Interferometry has been used to study a variety of physical effects, from the early experiments of Michelson and Morley that provided evidence to special relativity to the more recent gravity-wave detection devices used by the Laser Interferometer Gravitational-Wave Observatory (LIGO) experiment. The purpose of this thesis is to understand how one can exploit anyons and its unique characteristics to build interferometers, and understand whether there are immediate advantages in doing so. Anyons are two-dimensional quasiparticles known for their unusual fractional statistics and applications in quantum computing models. To study their usefulness in the context of interferometry, we present a quantum computational approach to interference experiments. Next we give an introduction to anyon models and how they can be used to perform universal quantum computing. We propose a quantum circuit which implements a certain type of interferometer, and how it can be realized in different anyon models. Finally, we discuss a quantum computing model based on linear optics with fermionic anyons that would enable the creation of a logical version of our interferometer in terms of a physical interferometer.