This paper proposes a new representation to explain and predict popularity evolution in social media. Recent work on social networks has led to insights about the popularity of a digital item. For example, both the content and the network matters, and gaining early popularity is critical. However, these observations did not paint a full picture of popularity evolution; some open questions include: what kind of popularity trends exist among different types of videos, and will an unpopular video become popular? To this end, we propose a novel phase representation that extends the well-known endogenous growth and exogenous shock model (Crane and Sornette 2008). We further propose efficient algorithms to simultaneously estimate and segment power-law shaped phases from historical popularity data. With the extracted phases, we found that videos go through not one, but multiple stages of popularity increase or decrease over many months. On a dataset containing the 2-year history of over 172,000 YouTube videos, we observe that phases are directly related to content type and popularity change, e.g., nearly 3/4 of the top 5% popular videos have 3 or more phases, more than 60% news videos are dominated by one long power-law decay, and 75% of videos that made a significant jump to become the most popular videos have been in increasing phases. Finally, we leverage this phase representation to predict future viewcount gain and found that using phase information reduces the average prediction error over the state-of-the-art for videos of all phase shapes.