  This article reviews the theoretical constraints on the scalar potential of a
general extension of the Standard Model that encompasses a $SU(3)_c\times
SU(3)_L\times U(1)_X$ gauge symmetry. In this respect, the
boundedness-from-below is analysed to identify the correct criteria for
obtaining the physical minima of the Higgs parameter space. Furthermore,
perturbativity and unitarity bounds are discussed in light of the exact
diagonalisation of the scalar fields. This study represents a framework for
fast numerical checks on specific $331$ Model benchmarks that are relevant for
future collider searches.
