Let R be a unital *-ring and let a, b, w ∈ R. In this paper, we give some new characterizations on w-core inverses in R. In particular, it is shown that a is w-core invertible if and only if it is w(aw) n−1-core invertible for any positive integer n, in which case, the representations of the w-core inverse and the w(aw) n−1-core inverse of a are both presented. We further characterize w-core inverses by Hermitian elements (or projections) and units.