10 years of Conformal Bootstrap

Conformal field theories have been long known to describe the fascinating universal physics of scale invariant critical points. For decades it has been a dream to study these intricate strongly coupled theories nonperturbatively using symmetries and other consistency conditions. This approach, called the conformal bootstrap, saw some successes in two dimensions but it is only in the last ten years that it has been fully realized in three, four, and other dimensions of interest.
In this talk I will review the basic ideas and the most important results obtained in the past years; I will discuss a few open questions that can be addressed with these techniques and present a few preliminary results.