  The discovery of Quantum Many-Body Scars (QMBS) both in Rydberg atom
simulators and in the Affleck-Kennedy-Lieb-Tasaki (AKLT) spin-1 chain model,
have shown that a weak violation of ergodicity can still lead to rich
experimental and theoretical physics. In this review, we provide a pedagogical
introduction to and an overview of the exact results on weak ergodicity
breaking via QMBS in isolated quantum systems with the help of simple examples
such as the fermionic Hubbard model. We also discuss various mechanisms and
unifying formalisms that have been proposed to encompass the plethora of
systems exhibiting QMBS. We cover examples of equally-spaced towers that lead
to exact revivals for particular initial states, as well as isolated examples
of QMBS. Finally, we review Hilbert Space Fragmentation, a related phenomenon
where systems exhibit a richer variety of ergodic and non-ergodic behaviors,
and discuss its connections to QMBS.
