Stimulated Brillouin scattering(SBS) is the main factor which limits the output power in narrow linewidth high power fiber amplifiers. Present SBS suppression methods and progress at home and abroad are illustrated, phase modulation to broaden the linewidth of the seed laser and the methods through applying gradient of temperature and strain to broaden the SBS gain spectrum are emphatically introduced, as well as some other methods such as acoustically tailored fiber. Finally, different approaches of SBS suppression are summarized and compared, which provides some references in related studies.