Typically, graded-index multimode fibers feature certain spatiotemporal nonlinear effects such as geometric parametric instability (GPI), which gradually expands the spectrum of transmitted laser light under certain conditions and eventually evolves into a supercontinuum. This paper introduces the concept of GPI and its physical connotations; moreover, the status of research on GPI-induced visible supercontinuum generation in graded-index multimode fibers is reviewed, and an analysis on the influence of fiber and pulse parameters on the output spectrum is presented. In addition to this, realizing an all-fiber structure and using short wavelength lasers as pump sources constitute key future research directions. Overall, the GPI-induced generation of the visible supercontinuum is expected to break through the power limitation of the supercontinuum generated by small core traditional photonic crystal fibers.