There has been increasing interest on the classification of arithmetically Cohen-Macaulay (for short aCM) sheaves on various projective varieties, which is important in a sense that the aCM sheaves are considered to give a measurement of complexity of the underlying space. A special type of aCM sheaves, called the Ulrich sheaves, are the ones achieving the maximum possible minimal number of generators. In this talk we classify the Ulrich vector bundles of arbitrary rank on smooth projective varieties of minimal degree. This is a joint work with M. Aprodu, S. Huh and J. Pons-Llopis)