With the exponential growth of online social network services such as Facebook and Twitter, social networks and social medias become more and more important, directly influencing politics, economics, and our daily life. Mining big social networks aims to collect and analyze web-scale social data to reveal patterns of individual and group behaviors. It is an inherently interdisciplinary academic field which emerged from sociology, psychology, statistics, and graph theory. In this article, I briefly survey recent progress on social network mining with an emphasis on understanding the interactions among users in the large dynamic social networks. I will start with some basic knowledge for social network analysis, including methodologies and tools for macro-level, meso-level and microlevel social network analysis. Then I will give an overall roadmap of social network mining. After that, I will describe methodologies for modeling user behavior including state-of-the-art methods forlearning user profiles, and introduce recent progress on modeling dynamics of user behaviors using deep learning. Then I will present models and algorithms for quantitative analysis on social interactions including homophily and social influence.Finally, I will introduce network structure model including social group formation, and network topology generation. We will introduce recent developed network embedding algorithms for modeling social networks with the embedding techniques. Finally, I will use several concrete examples from Alibaba, the largest online shopping website in the world, and WeChat, the largest social messaging service in China, to explain how online social networks influence our offline world.