Two finite words u and v are called Abelian equivalent if each letter occurs equally many times in both u and v. The Abelian subshift A_x of an infinite word x is the set of infinite words y such that, for each factor u of x, there exists a factor v of x which is Abelian equivalent to u. The notion of Abelian subshift gives a characterization of Sturmian words: among binary uniformly recurrent words, Sturmian words are exactly those words for which A^x equals the shift orbit closure. On the other hand, the Abelian subshift of the Thue-Morse word contains uncountably many minimal subshifts. In this paper we undertake a general study of Abelian subshifts. In particular, we characterize the Abelian subshifts of recurrent aperiodic balanced words and the Abelian subshifts of ternary words having factor complexity n+2 for all n=1.