  We study the constraints of crossing symmetry and unitarity in general 3D
Conformal Field Theories. In doing so we derive new results for conformal
blocks appearing in four-point functions of scalars and present an efficient
method for their computation in arbitrary space-time dimension. Comparing the
resulting bounds on operator dimensions and OPE coefficients in 3D to known
results, we find that the 3D Ising model lies at a corner point on the boundary
of the allowed parameter space. We also derive general upper bounds on the
dimensions of higher spin operators, relevant in the context of theories with
weakly broken higher spin symmetries.
