  We study the conformal bootstrap for a 4-point function of fermions
$\langle\psi\psi\psi\psi\rangle$ in 3D. We first introduce an embedding
formalism for 3D spinors and compute the conformal blocks appearing in fermion
4-point functions. Using these results, we find general bounds on the
dimensions of operators appearing in the $\psi \times \psi$ OPE, and also on
the central charge $C_T$. We observe features in our bounds that coincide with
scaling dimensions in the Gross-Neveu models at large $N$. We also speculate
that other features could coincide with a fermionic CFT containing no relevant
scalar operators.
