The large amount of text data which are continuously produced over time in a variety of large scale applications such as social networks results in massive streams of data. Typically massive text streams are created by very large scale interactions of individuals, or by structured creations of particular kinds of content by dedicated organizations. An example in the latter category would be the massive text streams created by news-wire services. Such text streams provide unprecedented challenges to data mining algorithms from an efficiency perspective. In this chapter, we review text stream mining algorithms for a wide variety of problems in data mining such as clustering, classification and topic modeling. We also discuss a number of future challenges in this area of research.