  The work is a brief review of the theory based on the $SU(3)_c \otimes
SU(3)_L \otimes U(1)_X$ gauge group in the presence of Heavy Leptons. Recent
analysis have established a set of four possible variants for the 3-3-1HL,
whose content arises according to the so-denoted variable $\beta$. Since it has
been argued about the presence of stable charged particles in this sort of
models, we divide the different sectors of the Lagrangian between universal and
specific vertices, and conclude that the omission of $\beta$-dependent terms in
the potential may induce to a discrete symmetry for the versions defined by
$|\beta|=\sqrt{3}$. In the context of $|\beta|=\frac{1}{\sqrt{3}}$, where the
new degrees of freedom have the same standard electric charges, additional
Yukawa interactions may create decay channels into the SM sector. Furthermore,
we introduce a method of diagonalization by parts in the Scalar sector
motivated by a general consequence of the Goldstone theorem. In summary, we
develop the most complete set of terms allowed by the symmetry group and
resolve their definitive pieces in order to justify the model description
present in the literature.
