Abstract: It has been conjectured in 1971 by Polyakov that critical phenomena have conformal invariance, both in two and three dimensions. While the two dimensional case has been intensely studied, the role of conformal invariance in d=3 is not fully clarified. We will describe which parts of conformal field theory carry over from d=2 to d=3. We will describe the `conformal bootstrap' equations, whose solutions should give conformally invariant algebras of local operators in d=3. The simplest case is the operator algebra corresponding to the critical point of the 3d Ising model. We conjecture that this operator algebra can be characterized by a minimal central charge condition. Numerical evidence for this conjecture will be presented. (based on arxiv:1403.4545).