Answering a question of Paul Erd\H{o}s, Antal Balog and Endre Szemerédi proved that a finite set $A \subset \mathbb{Z}$ with many three term arithmetic progressions must have a long arithmetic progression. We will discuss the proof of this result which uses the Balog-Szemer\'{e}di-Gowers Theorem, Freiman's Theorem, and Szemeredi's Theorem on arithmetic progressions. No previous knowledge of additive number theory will be assumed.