Structured sparsity, where the sparse parameters appear in a structured manner, has been a valuable modeling tool in various applications. Computationally, structured sparse penalties are more challenging to numerically cope with, mainly due to their nonsmoothness and non-separability. In this talk we give a systematic overview of some of the recent works centered on efficient algorithms and applications for structured sparsity. In particular, we show how the proximal map, the key component of a family of algorithms known as the proximal gradient (a.k.a. forward-backward splitting), can be computed through either smoothing, decomposition, or linear approximation. Some extensions to the nonconvex regime will be discussed and practical applications will be demonstrated. This is a to be co-presented by Eric Xing and Yaoliang Yu.