Complexity is all around us, whether it is the complexity of nature, the physical reality, the algorithms we develop, or the hardware architectures we use in computer graphics. Often times, however, only a fraction of this complexity is relevant for our perception, and trying to account for the rest mainly steals valuable computational resources, hindering our ability to generate more complex experiences. Therefore, it is no surprise that simpler solutions are often preferred and stand the test of time in computer graphics. Identifying the perceivable components of complexity is a vital research task, which is unique to computer graphics. This is the first step in developing simpler solutions for the complex problems we face. This talk is centered around the integral role of simplification and my general research philosophy in computer graphics. I will present many examples from my research, spanning modeling, animation, and rendering, with various forms of simplification for managing complexity, discuss the main ideas, and show how we could achieve improved computational efficiency, better visual fidelity, and/or more effective authoring techniques.