The invention of optical frequency combs (OFCs) based on femtosecond (fs) mode-locked lasers has merged laser based spectroscopy with fs-laser technology. OFCs have triggered quantum leaps of advancement in photonics, physics, astronomy, and engineering, while also lending themselves to applications in medical and environmental fields. The key feature of OFCs is their ultrahigh frequency and time resolution. In this review, we introduce the concept behind OFCs and their sources, with a focus on stability and phase-noise performance. We conclude with a discussion of recent progress of a monolithic OFC, which provides ultralow free-running phase noise and an unprecedented frequency stability of 1 part in 10 19 at a 1 s gate time.