In recent years, there has been renewed interest in the conformal bootstrap program, which uses crossing symmetry to constrain the data of unitary conformal field theories (in any dimension) by comparing different channels in which one can evaluate a four-point function. Most of the progress so far has been for four-point functions of scalar operators. I will review those constructions and discuss their limitations, explaining why we should be interested in non-scalar operators. Then I will explain how to construct all the ingredients needed to set up the next natural example: a four-point function of two scalars and two vectors.