Conformal Bootstrap in Fractional Dimensions

I will review the conformal bootstrap in fractional dimensions, with an emphasis on the Ising model in 1<d<2. I will discuss bounds on operator dimensions and compare the results with various theoretical and numerical models, in particular with resummed ε-expansion and Monte Carlo simulations of the Ising model on fractal lattices. I will also introduce some ongoing work on supersymmetric CFTs in 2<d<4.