Social networking sites such as Facebook or Twitter attract millions of users, who everyday post an enormous amount of content in the form of tweets, comments and posts. Since social network texts are usually short, learning tasks have to deal with a very high dimensional and sparse feature space, in which most features have low frequencies. As a result, extracting useful knowledge from such noisy data is a challenging task, that converts large-scale short-text learning tasks in social environments into one of the most relevant problems in machine learning and data mining. Feature selection is one of the most known and commonly used techniques for reducing the impact of the high dimensional feature space in text learning. A wide variety of feature selection techniques can be found in the literature applied to traditional, long-texts and document collections. However, short-texts coming from the social Web pose new challenges to this well-studied problem as texts� shortness offers a limited context to extract enough statistical evidence about words relations (e.g. correlation), and instances usually arrive in continuous streams (e.g. Twitter timeline), so that the number of features and instances is unknown, among other problems. This paper surveys feature selection techniques for dealing with short texts in both offline and online settings. Then, open issues and research opportunities for performing online feature selection over social media data are discussed.