The irrefutable success of deep learning on structured data (such as images and text) has sparked significant interest in its applicability to problems in geometry processing. In this talk, we will discuss the key challenges and current solutions for using mesh convolutional neural networks on the unstructured mesh representation for problems in geometry processing. We will outline the design choices and implications of (1) learning on different mesh elements (vertices, faces, edges); (2) invariance to rigid transformations; (3) invariance and equivariance to the order of mesh elements; (4) input features, among others. We discuss existing applications of mesh convolutional neural networks, as well as potential promising future directions.