We give a survey of current results on covering radius for sets of permutations with respect to the Hamming distance. Recall that given a subset S of a metric space X, the covering radius cr(S) of S is the smallest r such that the union of balls of radius r with centres at the elements of S covers the whole space X. Using a probabilistic method, we obtain a lower bound on the covering radius for certain sets of permutations. An application to intersecting families of permutations will be mentioned.