We define some new algebraic structures, termed colored Hopf algebras, by combining the coalgebra structures and antipodes of a standard Hopf algebra set ℋ, corresponding to some parameter set 𝒬, with the transformations of an algebra isomorphism group 𝒢, herein called color group. Such transformations are labeled by some color parameters, taking values in a color set 𝒞. We show that various classes of Hopf algebras, such as almost cocommutative, coboundary, quasitriangular, and triangular ones, can be extended into corresponding colored algebraic structures, and that colored quasitriangular Hopf algebras, in particular, are characterized by the existence of a colored universal ℛ-matrix, satisfying the colored Yang–Baxter equation. The present definitions extend those previously introduced by Ohtsuki, which correspond to some substructures in those cases where the color group is Abelian. We apply the new concepts to construct colored quantum universal enveloping algebras of both semisimple and nonsemisimple Lie algebras, considering several examples with fixed or varying parameters. As a by-product, some of the matrix representations of colored universal ℛ-matrices, derived in the present paper, provide new solutions of the colored Yang–Baxter equation, which might be of interest in the context of integrable models.