Abstract: We survey some recent graph algorithms that are based on picking a vertex at random and declaring it to be a part of the solution. This simple idea has been deployed to obtain state of-the-art parameterized, exact exponential time, and approximation algorithms for a number of problems, such as Feedback Vertex Set and Hitting Set. We will also discuss a recent 2 approximation algorithm for Feedback Vertex Set in Tournaments that is based on picking a vertex at random and declaring it to /not/ be part of the solution.