Challenges for the 3-3-1 models

The so-called 3-3-1 models have been widely studied in the literature. However, in almost all cases, as with other models, just simplified versions have been considered. On the other hand, the LHC has not neither confirmed nor rejected any model. In this paper we discuss some aspects of the 3-3-1 models that must be investigated, or be re-analyzed, firstly theoretically and, eventually, experimentally. Some of these issues are independent of the representation content of the particular model, that is, they are independent of the value of the $\beta$ parameter. However, others strongly depend on the particular model considered.