Given a collection of input rankings provided as permutations $\pi_i : [n] \rightarrow [n]$ for $1 \leq i \leq m$, the rank aggregation problem seeks to find another permutation $\sigma: [n] \rightarrow [n]$ that minimizes $\sum_{i=1}^m K(\sigma, \pi_i)$ where $K$ is the Kendall distance between the two permutations. In this talk, we will discuss motivation for the problem and some existing Markov chain based algorithms along with an investigation of their performance guarantees. Necessary background information will also be provided.