An optoelectronic oscillator (OEO) is a microwave photonic system that produces microwave signals with ultralow phase noise using a high-quality-factor optical energy storage element. This type of oscillator is desired in various practical applications, such as communication links, signal processing, radar, metrology, radio astronomy, and reference clock distribution. Recently, new mode control and selection methods based on Fourier domain mode-locking and parity-time symmetry have been proposed and experimentally demonstrated in OEOs, which overcomes the long-existing mode building time and mode selection problems in a traditional OEO. Due to these mode control and selection methods, continuously chirped microwave waveforms can be generated directly from the OEO cavity and single-mode operation can be achieved without the need of ultranarrowband filters, which are not possible in a traditional OEO. Integrated OEOs with a compact size and low power consumption have also been demonstrated, which are key steps toward a new generation of compact and versatile OEOs for demanding applications. We review recent progress in the field of OEOs, with particular attention to new mode control and selection methods, as well as chip-scale integration of OEOs.