Time-delayed optoelectronic oscillators are at the center of a large body of scientific literature. The complex behavior of these nonlinear oscillators has been thoroughly explored both theoretically and experimentally, leading to a better understanding of their dynamical properties. Beyond fundamental research, these systems have also inspired a wide and diverse set of applications, such as optical chaos communications, pseudorandom number generation, optoelectronic machine learning based on reservoir computing, ultrapure microwave generation, optical pulse-train synthesis, and sensing. The aim of this review is to provide a comprehensive survey of this field, to outline the latest achievements, and discuss the main challenges ahead.