The amount of 3D data is growing at an incredible rate, from scans to user-generated assets. However, many important geometry processing algorithms are not ready to handle this data, failing on low-quality inputs encountered in the wild. In this lecture, we’ll identify some of the challenges that make robust geometry processing hard, and discuss solutions and best practices using modern techniques. Topics will range from low-level challenges like floating point computation, to formalisms like improving finite element bases, to high-level applications like overfitting in geometric machine learning.