Stimulated Raman scattering is a mature technology that provides laser outputs with flexible wavelengths. Stable single-longitudinal-mode (SLM) Stokes is able to be achieved in a simply designed oscillator due to the nature of spatial hole burning free of Raman gain. Therefore, the Raman laser is considered as an attractive and potential method to generate SLM output with a particular wavelength. As the single-crystal diamond synthetic technology matures, high-power continuous-wave SLM diamond Raman lasers have been widely investigated for the past few years. In this review, the mechanism of Raman SLM operation in Raman oscillator and the state art of the SLM diamond Raman lasers are summarized. At last, the future investigations of continuous-wave SLM diamond Raman lasers are proposed.