We discuss continuous-wave single-frequency master oscillator -power amplifier (MOPA) sources based on ytterbium-doped fibers (YDFs) with particular attention to their recent dramatic advances and our up-to-date experimental results. This includes a 402 W planepolarized MOPA source and a 511 W random-polarized MOPA source. In these MOPAs, the final-stage high-power amplifier could operate with high efficiency of 70% -80% and even more, and a high gain of over 20 dB in a near diffraction-limited beam. We could see at least 7 dB enhancement of the stimulated Brillouin scattering (SBS) threshold for the 402 W polarization-maintaining (PM) YDF. In fact, we did not see any sign of SBS even at the highest output power. We eventually observed SBS appearance at around 500 W for the non-PM YDF. The observed SBS strengths were far weaker than expected in theory unless we allowed for the Brillouin gain reduction from thermal Brillouin gain broadening induced by the quantum-defect heating.