  The review is focused on one of the most exotic families of iron-based
superconductors belonging to the AFeAs structural type, where A is alkali
metal. We briefly concern physical and electron properties of the typical
members of this family, LiFeAs and NaFeAs, discuss the theoretical models
describing the multiple-gap superconducting state, and the experimental data
available in literature. As well, we specify the main unsolved problems, that
seem crucial for both the AFeAs family and for iron-based superconductors in
general.
