  We review a class of models in which the Standard Model (SM) is augmented by
vector-like leptons: one doublet and a singlet, which are odd under an unbroken
discrete $Z_2$ symmetry. As a result, the neutral component of these additional
vector-like leptons are stable and behave as dark matter. We study the
phenomenological constraints on the model parameters and elucidate the
parameter space for relic density, direct detection and collider signatures of
dark matter. In such models, we further add a scalar triplet of hypercharge two
and study the consequences. In particular, after electro weak symmetry breaking
(EWSB), the triplet scalar gets an induced vacuum expectation value (vev),
which yield Majorana masses not only to the light neutrinos but also to
vector-like leptonic doublet DM. Due to the Majorana mass of DM, the $Z$
mediated elastic scattering with nucleon is forbidden and hence allowing the
model to survive from stringent direct search bound. The DM without scalar
triplet lives in a small singlet-doublet leptonic mixing region ($\sin\theta
\le 0.1$) due to large contribution from singlet component and have small mass
difference ($\Delta m \sim 10$ GeV) with charged companion, the NLSP (next to
lightest stable particle), to aid co-annihilation for yielding correct relic
density. Both these observations change to certain extent in presence of scalar
triplet to aid observability of hadronically quiet leptonic final states at
LHC, while one may also confirm/rule-out the model through displaced vertex
signal of NLSP, a characteristic signature of the model in relic density and
direct search allowed parameter space.
