Euclidean scattering transform was introduced nearly a decade ago to improve the mathematical understanding of the success of convolutional neural networks (ConvNets) in image data analysis and other tasks. Inspired by recent interest in geometric deep learning, which aims to generalize ConvNets to manifold and graph-structured domains, we generalize the scattering transform to graphs and  manifolds. In this talk, I'll introduce the application of our geometric scattering methods in graph classification of social network data, and in data exploration of biochemistry data; in addition, I'll demonstrate the use of geometric scattering features in providing useful manifold signal descriptors for several tasks involving classification of manifolds or signals over them.