Explore simplicial neural networks (SNNs), a groundbreaking extension of graph neural networks, in this 52-minute conference talk. Delve into the world of topological spaces called simplicial complexes, which encode higher-order interactions beyond pairwise relationships. Learn how SNNs can process richer data structures, including vector fields and n-fold collaboration networks. Discover the novel concept of simplicial convolution and its application in constructing advanced convolutional neural networks. Examine the practical application of SNNs in imputing missing data on coauthorship complexes. Gain insights into Laplacians for simplicial complexes, the architecture of SNNs, and their accuracy in predicting missing citations. Conclude with an overview of other topological neural networks and potential future directions in this exciting field of applied algebraic topology.