Echo chambers, i.e., situations where one is exposed only to opinions that agree with their own, are an increasing concern for the political discourse in many democratic countries. This paper studies the phenomenon of political echo chambers on social media. We identify the two components in the phenomenon: the opinion that is shared ('echo'), and the place that allows its exposure ('chamber' --- the social network), and examine closely at how these two components interact. We define a production and consumption measure for social-media users, which captures the political leaning of the content shared and received by them. By comparing the two, we find that Twitter users are, to a large degree, exposed to political opinions that agree with their own. We also find that users who try to bridge the echo chambers, by sharing content with diverse leaning, have to pay a 'price of bipartisanship' in terms of their network centrality and content appreciation. In addition, we study the role of 'gatekeepers', users who consume content with diverse leaning but produce partisan content (with a single-sided leaning), in the formation of echo chambers. Finally, we apply these findings to the task of predicting partisans and gatekeepers from social and content features. While partisan users turn out relatively easy to identify, gatekeepers prove to be more challenging.