Optical delay lines (ODLs) are one of the key enabling components in photonic integrated circuits and systems. They are widely used in time-division multiplexing, optical signal synchronization and buffering, microwave signal processing, beam forming and steering, etc. The development of integrated photonics pushes forward the miniaturization of ODLs, offering improved performances in terms of stability, tuning speed, and power consumption. The integrated ODLs can be implemented using various structures, such as single or coupled resonators, gratings, photonic crystals, multi-path switchable structures, and recirculating loop structures. The delay tuning in ODLs is enabled by either changing the group refractive index of the waveguide or changing the length of the optical path. This paper reviews the recent development of integrated ODLs with a focus on their abundant applications and flexible implementations. The challenges and potentials of each type of ODLs are pointed out.