  The longer-lived excited nuclear states, referred as nuclear isomers, exist
due to the hindered decays owing to their peculiar nucleonic structural
surroundings. Some of these conditions, being exceptionally rare and limited to
achieve, elevate certain isomers to the status of extreme and unusual isomers
among their kin. For example, the $E5$ coupling of single-particle orbitals is
rare and so are $E5$ decaying isomers. This review delves into some of such
remarkable isomers scattered across the nuclear landscape while highlighting
the possibilities to find more of them. Unique properties of some of them,
harbor the potential for transformative applications in medicine and energy. An
exciting example is that of the lowest energy isomer known so far in
$^{229}$Th, which may help realize the dream of an ultra-precise nuclear clock
in the coming decade. These isomers also offer an insight into the extremes of
nuclear structure associated with them, which leads to their unusual status in
energy, half-life, spin etc. The review attempts to highlight isomers with
high-multipolarities, high-spins, high-energies, longest half-lives, extremely
low energy, etc. A lack of theoretical understanding of the decay rates,
half-lives and moments of these isomers is also pointed out.
