Abstract: In 1963, Corrádi and Hajnal verified a conjecture of Erdős by showing that for every \(k \in \mathbb{Z}\), if an \(n\)-vertex graph \(G\) satisfies \(n \ge 3k\) and \(\delta(G) \ge 2k\), then \(G\) will contain \(k\) disjoint cycles.  This result is extremely tight and has served as the motivation behind a great deal of research in recent years.  In this talk, we will discuss only a few of these extensions with an emphasis on their sharpness.  Time permitting, we will also talk about recent extensions into hypergraphs.