  Thanks to the impressive progress of conformal bootstrap methods we have now
very precise estimates of both scaling dimensions and OPE coefficients for
several 3D universality classes. We show how to use this information to obtain
similarly precise estimates for off-critical correlators using conformal
perturbation. We discuss in particular the $< \sigma (r) \sigma (0) >$, $<
\epsilon (r) \epsilon (0) >$ and $< \sigma (r) \epsilon (0) >$ two point
functions in the high and low temperature regimes of the 3D Ising model and
evaluate the leading and next to leading terms in the $s = t r^{\Delta_{t}}$
expansion, where $t$ is the reduced temperature. Our results for $< \sigma (r)
\sigma (0) >$ agree both with Monte Carlo simulations and with a set of
experimental estimates of the critical scattering function.
