  The triplet or type-II seesaw mechanism is the simplest way to endow
neutrinos with mass in the Standard Model (SM). Here we review its associated
theory and phenomenology, including restrictions from $S$, $T$, $U$ parameters,
neutrino experiments, charged lepton flavour violations as well as collider
searches. We also examine restrictions coming from requiring consistency of
electroweak symmetry breaking, i.e. perturbative unitarity and stability of the
vacuum. Finally, we discuss novel effects associated to the scalar mediator of
neutrino mass generation namely, (i) rare processes, e.g. $l_\alpha \to l_\beta
\gamma$ decays, at the intensity frontier, and also (ii) four-lepton signatures
in colliders at the high-energy frontier. These can be used to probe neutrino
properties in an important way, providing a test of the absolute neutrino mass
and mass-ordering, as well as of the atmospheric octant. They may also provide
the first evidence for charged lepton flavour violation in nature. In contrast,
neutrino non-standard interaction strengths are found to lie below current
detectability.
