Abstract: Shrinking target sets arise from Iterated Function Systems associated to Diophantine approximation. In this talk we will prove a formula for the Hausdorff dimension of such a set associated to a non-autonomous IFS on the interval. The proof presented appears in a forthcoming paper by Fishman, Mance, Simmons, and Urbański, and it illustrates how the well-known Mass Distribution Principle can be used to obtain lower bounds on the HD of sets.