High-brightness fiber laser sources usually utilize active rare-earth-doped fibers cladding-pumped by multimode laser diodes (LDs), but they operate in limited wavelength ranges. Singlemode-passive-fiber based Raman lasers are able to operate at almost any wavelength being pumped by high-power fiber lasers. One of the interesting possibilities is to directly pump graded-index (GRIN) multimode passive fibers by available high-power multimode LDs at 915–940 nm, thus achieving high-power Raman lasing in the wavelength range of 950–1000 nm, which is problematic for rare-earth-doped fiber lasers. Here we review the latest results on the development of all-fiber high-brightness LD-pumped sources based on GRIN fiber with in-fiber Bragg gratings (FBGs). The mode-selection properties of FBGs inscribed by fs pulses supported by the Raman clean-up effect result in efficient conversion of multimode pump into a high-quality output beam at 9xx nm. GRIN fibers with core diameters 62.5, 85 and $100~\unicode[STIX]{x03BC}\text{m}$ are compared. Further scaling capabilities and potential applications of such sources are discussed.