Social networks are pervasive and encompass interactions over online social media, human links in epidemic processes, terrorist cells, and collaborations among researchers. The value in understanding and predicting complex network behavior cannot be understated, thanks to the growing role of search engines, cyber warfare, online marketing, and social recommendation tools. Real-world social networks are fraught with unique challenges that limit the efficacy of contemporary tools. For example, such networks are big (billions of nodes), evolve over time, and are often not directly observable. Viewed through a statistical learning lens, many network analytics problems boil down to (non-) parametric regression and classification, dimensionality reduction, or clustering. Adopting this point of view, this talk will put forth novel learning approaches for network visualization, anomaly and community detection, prediction of network processes, and dynamic network inference. Key emphasis will be placed on parsimonious models exploiting sparsity, low rank, or low-dimensional manifolds, attributes that have been shown useful for complexity reduction. The merits of the novel schemes will be demonstrated on both simulated and real-world social networks.