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We review our recent experimental results on the cascaded Raman conversion of highly multimode laser diode (LD) pump radiation into the first- and higher-order Stokes radiation in multimode graded-index fibers. A linear cavity composed of fiber Bragg gratings (FBGs) inscribed in the fiber core is formed to provide feedback for the first Stokes order, whereas, for the second order, both a linear cavity consisting of two FBGs and a half-open cavity with one FBG and random distributed feedback (RDFB) via Rayleigh backscattering along the fiber are explored. LDs with different wavelengths (915 and 940 nm) are used for pumping enabling Raman lasing at different wavelengths of the first (950, 954 and 976 nm), second (976, 996 and 1019 nm) and third (1065 nm) Stokes orders. Output power and efficiency, spectral line shapes and widths, beam quality and shapes are compared for different configurations. It is shown that the RDFB cavity provides higher slope efficiency of the second Stokes generation (up to 70% as that for the first Stokes wave) with output power up to ~30 W, limited by the third Stokes generation. The best beam quality parameter of the second Stokes beam is close to the diffraction limit (M2~1.3) in both linear and half-open cavities, whereas the line is narrower (