  As the Higgs boson properties settle, the constraints on the Standard Model
extensions tighten. We consider all possible new fermions that can couple to
the Higgs, inspecting sets of up to four chiral multiplets. We confront them
with direct collider searches, electroweak precision tests, and current
knowledge of the Higgs couplings. The focus is on scenarios that may depart
from the decoupling limit of very large masses and vanishing mixing, as they
offer the best prospects for detection. We identify exotic chiral families that
may receive a mass from the Higgs only, still in agreement with the
$h\gamma\gamma$ signal strength. A mixing $\theta$ between the Standard Model
and non-chiral fermions induces order $\theta^2$ deviations in the Higgs
couplings. The mixing can be as large as $\theta\sim 0.5$ in case of custodial
protection of the $Z$ couplings or accidental cancellation in the oblique
parameters. We also notice some intriguing effects for much smaller values of
$\theta$, especially in the lepton sector. Our survey includes a number of
unconventional pairs of vector-like and Majorana fermions coupled through the
Higgs, that may induce order one corrections to the Higgs radiative couplings.
We single out the regions of parameters where $h\gamma\gamma$ and $hgg$ are
unaffected, while the $h\gamma Z$ signal strength is significantly modified,
turning a few times larger than in the Standard Model in two cases. The second
run of the LHC will effectively test most of these scenarios.
