An optoelectronic oscillator (OEO) is an optoelectronic hybrid oscillator which utilizes ultra-low loss fiber as an electro-magnetic energy storage element, overcoming the limits of traditional microwave oscillators in phase noise performance. Due to their ability to generate ultra-low phase noise microwave signal, optoelectronic oscillators have attracted considerable attentions and are becoming one of the most promising and powerful microwave signal sources. In this paper, we briefly introduce the operation principle and discuss current research on frequency stability and spurious suppression of optoelectronic oscillators.