Given a population network and current infection data of a contagious disease like flu, how to effectively allocate vaccines? What if the infection patterns change? Can we guess if a user is sick from her tweet? How to find failure 'hotspots' in energy grids? How do we quickly zoom out of a graph?  Answering all these questions involves the study of aggregated ‘propagation (cascade)’-based dynamics over complex connectivity patterns. As diverse as these problems sound, they can all be approached using modern tools of network science and dynamics. Networks are powerful tools for modeling processes and situations of interest in real-life. They are ubiquitous, from online social networks, power-grids, to router graphs. Dynamical processes on networks are also widespread across several domains. Understanding such propagation processes will eventually enable us to manipulate them for our benefit e.g., understanding dynamics of epidemic spreading over graphs helps design more robust policies for immunization. 

In this talk we will focus on leveraging propagation-style processes on large networks to understand, predict and manage behaviors. We present a multi-pronged approach, which includes: (a) Theoretical results on the behavior of fundamental models; (b) Scalable Algorithms based on these processes e.g., immunization, finding critical nodes, correcting noisy data, improving e-commerce query relevance; and (c) Empirical Studies using social media like Facebook and malware databases like at Symantec. We finally conclude with future research directions. The problems we focus on are central in many diverse areas: from epidemiology and public health, critical infrastructure systems to information dissemination.