  We investigate dynamical quantum phase transitions in disordered quantum
many-body models that can support many-body localized phases. Employing
$l$-bits formalism, we lay out the conditions for which singularities
indicative of the transitions appear in the context of many-body localization.
Using the combination of the mapping onto $l$-bits and exact diagonalization
results, we explicitly demonstrate the presence of these singularities for a
candidate model that features many-body localization. Our work paves the way
for understanding dynamical quantum phase transitions in the context of
many-body localization, and elucidating whether different phases of the latter
can be detected from analyzing the former. The results presented are
experimentally accessible with state-of-the-art ultracold-atom and ion-trap
setups.
