We study the F-regularity of Rees algebras R(I) = A[It] in terms of the global F-regularity of the blowing-up X = Proj R(I) of Spec A. As it reads, global F-regularity is a global analog of strong F-regularity defined via splitting of Frobenius maps in prime characteristic, and these notions are extended to characteristic zero by reduction modulo p much greater than 0. We study in detail the case where (A, in) is a two-dimensional local ring and I is an m-primary ideal. In characteristic zero, the condition for R(I) to have F-regular type is described in terms of the dual graph of a resolution (X) over tilde on which Itheta((X) over tilde) is invertible. We also prove some miscellaneous results concerning singularities of Rees algebras and extended Rees algebras of higher dimension. (C) 2002 Elsevier Science.