Computer graphics, as routinely seen in movies nowadays, involves increasingly sophisticated numerics. While differential equations used to model reality can be numerically simulated in countless manners, the geometric structures these equations are supposed to preserve are often lost in the process. Through various vignettes describing recent developments, I will argue for a geometric, variational approach to graphics and computational physics for improved numerics and robustness: besides blurring the line between continuous mathematics and the resolutely discrete nature of digital data, a discrete variational approach to geometry is a powerful tool for applications. The importance of approaching computations through the lens of geometry will be a recurring theme throughout the talk.