In this talk, I will discuss a new tool in graph cut algorithms called the isolating cuts lemma. Originally developed for the (global) minimum cut problem, the isolating cuts lemma has been a key ingredient in recent progress on longstanding questions in problems such as all-pairs minimum cuts, Steiner connectivity, and connectivity augmentation. I will give a simple proof of the lemma and describe applications to some of the problems mentioned above. The talk will be self-contained.