Link recommendation has attracted significant attentions from both industry practitioners and academic researchers. In industry, link recommendation has become a standard and most important feature in online social networks, prominent examples of which include "People You May Know" on LinkedIn and "You May Know" on Google+. In academia, link recommendation has been and remains a highly active research area. This paper surveys state-of-the-art link recommendation methods, which can be broadly categorized into learning-based methods and proximity-based methods. We further identify social and economic theories, such as social interaction theory, that underlie these methods and explain from a theoretical perspective why a link recommendation method works. Finally, we propose to extend link recommendation research in several directions that include utility-based link recommendation, diversity of link recommendation, link recommendation from incomplete data, and experimental study of link recommendation.