  It is well-known that at tree-level the d=5 Weinberg operator can be
generated in exactly three different ways, the famous seesaw models. In this
paper we study the related question of how many phenomenologically consistent
1-loop models one can construct at d=5. First, we discuss that there are two
possible classes of 1-loop neutrino mass models, that allow avoiding stable
charged relics: (i) Models with dark matter candidates and (ii) models with
"exits". Here, we define "exits" as particles that can decay into standard
model fields. Considering 1-loop models with new scalars and fermions, we find
in the dark matter class a total of (113+205) models, while in the exit class
we find (38+368) models. Here, 113 is the number of DM models, which require a
stabilizing symmetry, while 205 is the number of models which contain a dark
matter candidate, which maybe accidentally stable. In the exit class the 38
refers to models, for which one (or two) of the internal particles in the loop
is a SM field, while the 368 models contain only fields beyond the SM (BSM) in
the neutrino mass diagram. We then study the RGE evolution of the gauge
couplings in all our 1-loop models. Many of the models in our list lead to
Landau poles in some gauge coupling at rather low energies and there is exactly
one model which unifies the gauge couplings at energies above $10^{15}$ GeV in
a numerically acceptable way.
