The European Union Emission Trading Scheme (EU ETS) is the first large scale CO2 emission trading system in the world. Carbon allowances are financial assets, potentially vulnerable to the behavior of traders and investors. In fact, the carbon price has been quite volatile since the inception of the market, and it has recently hit very low values. However, to date, no work exists to evaluate whether volatility and price spikes are due to episodes of speculation and price bubbles. Our paper fills this gap. We use the recent approaches developed by Phillips and Yu (2010), Phillips et al. (2011), and Phillips et al. (2015a, 2015b) who propose a recursive right sided unit root approaches to detect and date-stamp mildly explosive behaviors and carbon market exuberance. We complement this methodology by using the wild bootstrap procedure by Gongalves and Kilian (2004) to control for the heteroschedasticity of carbon price data. Analyzing the EU ETS front month contract price, from 2005 to 2014, we find different episodes of price bubbles. These episodes are not explained by similar behavior of the fundamentals but seem related to energy and environmental policy announcements. Our results can provide insightful policy implications in the context of the actual carbon market reform, as well as the implementation of stricter financial regulations rules to CO2 trading.