  We discuss the simplest mechanisms for generating neutrino masses at tree
level and one loop level. We find a significant number of new possibilities
where one can generate neutrino masses at the one-loop level by adding only two
new types of representations. These models have renormalizable interactions
that automatically conserve baryon number. Adding to the minimal standard model
a scalar color octet with SU(3) X SU(2) X U(1) quantum numbers, (8,2,1/2), and
a fermionic color octet in the fundamental or adjoint representation of SU(2)
one can generate neutrino masses in agreement with the experiment. Signals at
the LHC, and constraints from flavour violation are briefly discussed.
