Semiconductor lasers are widely used in incoherent/coherent optical communications, optical fiber sensing, and lidar due to their small size, high efficiency, and immunity to vibrations. To support the continuous evolution of these high-performance application systems, the noise characteristics of semiconductor lasers play a key role and the noise levels need to be reduced to unprecedentedly low values (such as quantum limit). In this paper, a comprehensive overview on the principles, measurements, and suppressions of semiconductor laser noises are provided. First, we introduce the analysis models and key performance indicators of semiconductor lasers related to noise. Then, different noise measurement systems are investigated for semiconductor lasers and the noise characteristics are fully analyzed. Next, the noise suppression methods towards semiconductor lasers are demonstrated from three aspects: the chip structures, the external cavity optical feedback technology and the driving and controlling circuits. Finally, we summarize the recent advances on the noise measurement and suppression of semiconductor laser, future prospects are also discussed.