In recent years we have witnessed a revival of the conformal bootstrap approach to CFTs. I will discuss the application of these ideas to six-dimensional conformal field theories with (2,0) supersymmetry, focusing on the universal four-point function of stress tensor multiplets. For these theories the program splits into an analytic and a numerical component. The analytic component yields exact results but in a protected subsector. The numerical component can be used to derive bounds on OPE coefficients and scaling dimensions from the constraints of crossing symmetry and unitarity. The principal numerical result is strong evidence that the A1 theory realizes the minimal allowed central charge (c=25) for any interacting (2,0) theory. This implies that the full stress tensor four-point function of the A1 theory is the unique unitary solution to the crossing symmetry equation at c=25. For this theory, we can estimate the scaling dimensions of the lightest unprotected operators appearing in the stress tensor operator product expansion. We also find rigorous upper bounds for dimensions and OPE coefficients for a general interacting (2,0) theory of central charge c. For large c, our bounds appear to be saturated by the holographic predictions obtained from eleven-dimensional supergravity.