###### Abstract  
After five decades of development, mode-locked lasers have become significant building blocks for many optical systems in scientific research, industry, and biomedicine. Advances in noise measurement and reduction are motivated for both shedding new light on the fundamentals of realizing ultra-low-noise optical frequency combs and their extension to potential applications for standards, metrology, clock comparison, and so on. In this review, the theoretical models of noise in mode-locked lasers are first described. Then, the recent techniques for timing jitter, carrier-envelope phase noise, and comb-line noise measurement and their stabilization are summarized. Finally, the potential of the discussed technology to be fulfilled in novel optical frequency combs, such as electro-optic (EO) modulated combs, microcombs, and quantum cascade laser (QCL) combs, is envisioned.  
mode-locked laser; noise measurement; optical frequency comb Permission 10.0.  
standards [19, 20]. An accurate long-distance timing-standard transfer is crucial in large-scale scientific instruments, such as the synchronous laser-microwave networks in X-ray free-electron lasers [21] and coherent aperture synthesis [22]. In addition, femtosecond lasers with low timing jitter are also significant laser sources for high-precision optical sampling and photonic analog-to-digital converters [23], photonic radar [24], and optical interconnections [25].  
The stability of the pulse envelope's electric field phase is also important when the pulse duration is approaching or even shorter than a single optical cycle [26]. Therefore, carrier-envelope phase stabilization is essential in applications such as coherent beam combination [27, 28], multi-channel coherent pulse synthesis to generate few-cycle pulses [29, 30, 31], and arbitrary waveform generation [32]. Meanwhile, in extreme X-ray pulse generation [33, 34, 35], attosecond metrology [36], and extreme nonlinear optics [37], the phase stability of femtosecond pulses also plays a vital role. Optical pulses with a stable carrier-envelope phase can also be utilized as practical measurement tools. In 2016, [PERSON] et al. inserted an electro-optic crystal in a Ti:sapphire femtosecond laser cavity and measured the Kerr constant of the electro-optic crystal by monitoring the change of the laser's carrier-envelope offset frequency [38]. Later, [PERSON] et al. realized the measurement of the Doppler effect of the intracavity pulse [39].  
For the above reasons, noise measurement and reduction in mode-locked lasers are extremely essential for various applications. In this review, these are investigated from the aspect of repetition rate, carrier-envelope phase, and comb-line noise.  
The rest of this review is organized as follows. In Section 2, theoretical models describing timing jitter, carrier-envelope phase noise, and comb-line noise in mode-locked lasers are provided. Detailed noise measurement and reduction methods for the three above-mentioned types of noise are introduced in Section 3. Finally, in Section 4, a selection of near-future trends and prospects for noise reduction in novel mode-locked lasers are envisioned.