  We analyse the general structure of the three-point functions involving
conserved bosonic and fermionic higher-spin currents in three-dimensional
conformal field theory. Using the constraints of conformal symmetry and
conservation equations, we use a computational formalism to analyse the general
structure of $\langle J^{}_{s_{1}} J'_{s_{2}} J''_{s_{3}} \rangle$, where
$J^{}_{s_{1}}$, $J'_{s_{2}}$ and $J''_{s_{3}}$ are conserved currents with
spins $s_{1}$, $s_{2}$ and $s_{3}$ respectively (integer or half-integer). The
calculations are completely automated for any chosen spins and are limited only
by computer power. We find that the correlation function is in general fixed up
to two independent even structures, and one odd structure, subject to a set of
triangle inequalities. We also analyse the structure of three-point functions
involving higher-spin currents and fundamental scalars and spinors.
