This tutorial presents a guided tour of laser feedback interferometry, from its origin and early development through its implementation to a slew of sensing applications, including displacement, distance, velocity, flow, refractive index, and laser linewidth measurement. Along the way, we provide a step-by-step derivation of the basic rate equations for a laser experiencing optical feedback starting from the standard Lang and Kobayashi model and detail their subsequent reduction in steady state to the excess-phase equation. We construct a simple framework for interferometric sensing applications built around the laser under optical feedback and illustrate how this results in a series of straightforward models for many signals arising in laser feedback interferometry. Finally, we indicate promising directions for future work that harnesses the self-mixing effect for sensing applications.