Segmentation, referring to separating image features from backgrounds, is one of the most important tasks in many image processing fields including computer vision and medical imaging. In this talk we present two related multigrid algorithms for multiphase image segmentation. Algorithm I solves the model by Vese-Chan (Commu. Pure Appl. Math., 2002). We first generalize our recently developed multigrid method to this multiphase segmentation model (MG1); we also give a local Fourier analysis for the local smoother which leads to a new and more effective smoother. Although MG1 is found many magnitudes faster than the fast method of additive operator splitting (AOS); both algorithms are not robust with regard to the initial guess. To overcome this dependence on the initial guess, we consider a hierarchical segmentation model M. Jeon, M. Alexander, W. Pedrycz and N. Pizzi (Pattern Recognition Letters, 2005) which achieves multiphase segmentation by repeated use of the Chan-Vese two-phase model (IEEE IP 2001); our Algorithm II solves this model by a multigrid algorithm (MG2). Various experiments will show that both algorithms are efficient and in particular MG2 is more robust than MG1 with respect to initial guesses. Our methods are many orders of magnitude faster than competing methods.