  We consider a class of models in which the neutrinos acquire Majorana masses
through mixing with singlet neutrinos that emerge as composite states of a
strongly coupled hidden sector. In this framework, the light neutrinos are
partially composite particles that obtain their masses through the inverse
seesaw mechanism. We focus on the scenario in which the strong dynamics is
approximately conformal in the ultraviolet, and the compositeness scale lies at
or below the weak scale. The small parameters in the Lagrangian necessary to
realize the observed neutrino masses can naturally arise as a consequence of
the scaling dimensions of operators in the conformal field theory. We show that
this class of models has interesting implications for a wide variety of
experiments, including colliders and beam dumps, searches for lepton flavor
violation and neutrinoless double beta decay, and cosmological observations. At
colliders and beam dumps, this scenario can give rise to striking signals
involving multiple displaced vertices. The exchange of hidden sector states can
lead to observable rates for flavor violating processes such as $\mu
\rightarrow e \gamma$ and $\mu \rightarrow e$ conversion. If the compositeness
scale lies at or below a hundred MeV, the rate for neutrinoless double beta
decay is suppressed by form factors and may be reduced by an order of magnitude
or more. The late decays of relic singlet neutrinos can give rise to spectral
distortions in the cosmic microwave background that are large enough to be
observed in future experiments.
