Abstract: I will talk about a few applications where topological features play an important role, including emphasis on computational aspects. In sensor networks, I will show how combinatorial Laplacians can be effectively used to find coverage holes and compute persistence of homological features to improve robustness. I will then discuss the relation between restricted Delaunay triangulation and alpha complexes, and its implications in networks. I think Topology will play a major role in signal processing and social networks, and we are beginning to see these connections. In signal processing, the entry point for Topology is the delay embedding, where a signal is converted into a point cloud. I will talk about about a simple application of detecting wheezes in breathing signals using this approach, and then share my view of future of topology (and geometry) in signal processing. In social networks, I will present some of our recent findings on how topology influences the core periphery decomposition of a network, and helps in detecting communities.