  Spin-orbit effects in heavy 5$d$ transition metal oxides, in particular,
iridates, have received enormous current interest due to the prediction as well
as the realization of a plethora of exotic and unconventional magnetic
properties. While a bulk of these works are based on tetravalent iridates
($d^5$), where the counter-intuitive insulating state of the rather extended
5$d$ orbitals are explained by invoking strong spin-orbit coupling, the recent
quest in iridate research has shifted to the other valencies of Ir, of which
pentavalent iridates constitute a notable representative. In contrast to the
tetravalent iridates, spin-orbit entangled electrons in $d^4$ systems are
expected to be confined to the $J = 0$ singlet state without any resultant
moment or magnetic response. However, it has been recently predicted that,
magnetism in $d^4$ systems may occur via magnetic condensation of excitations
across spin-orbit-coupled states. In reality, the magnetism in Ir$^{5+}$
systems are often quite debatable both from theoretical as well as experimental
point of view. Here we provide a comprehensive overview of the spin-orbit
coupled $d^4$ model systems and its implications in the studied pentavalent
iridates. In particular, we review here the current experimental and
theoretical understanding of the double perovskite ($A_2B$YIrO$_6$, $A =$ Sr,
Ba, $B =$Y, Sc, Gd), 6H-perovskite (Ba$_3M$Ir$_2$O$_9$, $M =$ Zn, Mg, Sr, Ca),
post-perovskite (NaIrO$_3$), and Hexagonal (Sr$_3$MIrO$_6$) iridates, along
with a number of open questions that require future investigation.
