  We define form factors and scattering amplitudes in Conformal Field Theory as
the coefficient of the singularity of the Fourier transform of time-ordered
correlation functions, as $p^2 \to 0$. In particular, we study a form factor
$F(s,t,u)$ obtained from a four-point function of identical scalar primary
operators. We show that $F$ is crossing symmetric, analytic and it has a
partial wave expansion. We illustrate our findings in the 3d Ising model,
perturbative fixed points and holographic CFTs.
