Abstract: Permutation codes under different metrics have been widely studied. In particular, due to their applications in the rank-modulation schemes for flash memories, we consider permutation codes under Kendall's $\tau$-metric, which is the minimum number of adjacent transpositions to transform one permutation into the other. In this talk I will briefly go over some known results on permutation codes under Kendall's $\tau$-metric, including bounds derived via a graph-theoretic approach.