  The iron-based superconductors that contain FeAs layers as the fundamental
building block in the crystal structures have been rationalized in the past
using ideas based on the Fermi Surface nesting of hole and electron pockets
when in the presence of weak Hubbard $U$ interactions. This approach seemed
appropriate considering the small values of the magnetic moments in the parent
compounds and the clear evidence based on photoemission experiments of the
required electron and hole pockets. However, recent results in the context of
alkali metal iron selenides, with generic chemical composition
$A_x$Fe$_{2-y}$Se$_2$ ($A$ = alkali element), have drastically challenged those
previous ideas since at particular compositions $y$ the low-temperature ground
states are insulating and display antiferromagnetic magnetic order with large
iron magnetic moments. Moreover, angle resolved photoemission studies have
revealed the absence of hole pockets at the Fermi level in these materials. The
present status of this exciting area of research, with the potential to alter
conceptually our understanding of the iron-based superconductors, is here
reviewed, covering both experimental and theoretical investigations. Other
recent related developments are also briefly reviewed, such as the study of
selenide two-leg ladders and the discovery of superconductivity in a single
layer of FeSe. The conceptual issues considered established for the alkali
metal iron selenides, as well as the several issues that still require further
work, are discussed in the text.
