Highly accurate {\it ab initio} calculations have been performed for the electronic ground state and the first two excited states of the helium trimer cation, He$_3^+$. The three body potential energy surfaces are represented analytically using standard formulae with the adjustable parameters estimated via the least-squares fitting procedure and used in semi-empirical modellings of larger ionized clusters of helium. It is well known that the inclusion of the three-body interactions is crucial for describing the intra-cluster interactions in He$_n^+$ complexes correctly. Accordingly, a semiempirical {\it triatomics-in-molecule} model, within which the three-body contributions are taken into account explicitly, is developed for the helium cluster cations and employed subsequently in modellings of interactions and the electronic and geometric structure of these clusters.