Fox and Milnor showed that the classical Alexander polynomial of a knot K in S^3 can obstruct K from bounding a smooth disk in B ^4 . Twisted Alexander polynomials provides further information about four-dimensional aspects of classical knots. This information is most easily formulated in terms of the knot concordance group. This talk will be a survey of some of the uses of the twisted polynomial in studying properties of knot concordance. The talk will include a discussion of the affects of knot reversal and mutation on concordance, the classification of low-crossing number knots in the concordance group, and doubly slicing knots. The results represent joint work with Julia Collins, Paul Kirk, and Jeff Meier.