In this talk, we follow Galashin and Pylyavskyy's paper to give an elementary criterion and a classification of bipartite recurrent quivers that exhibit periodicity of T-systems. After reviewing some prerequisites, we will first state the graph theoretical condition for periodicity and discuss the classification. Here we will see a reappearance of a periodicity result presented by Bernhard Keller in his colloquium talk last week. Then, we will discuss three other equivalent conditions for periodicity and their significance through several examples. A quick sketch of the proof of the main theorem will be given if time permits.