  A dislocation, just like a phonon, is a type of atomic lattice displacement
but subject to an extra topological constraint. However, unlike the phonon
which has been quantized for decades, the dislocation has long remained
classical. This article is a comprehensive review of the recent progress on
quantized dislocations, aka the "dislon" theory. Since the dislon utilizes
quantum field theory to solve materials defects problems, we adopt a
pedagogical approach to facilitate understanding for both materials science and
condensed matter communities. After introducing a few preliminary concepts of
dislocations, we focus on the necessity and pathways of dislocation's
quantization in great detail, followed by the interaction mechanism between the
dislon and materials electronic and phononic degrees of freedom. We emphasize
the formality, the new phenomena, and the predictive power. Imagine the leap
from classical lattice wave to quantized phonon; the dislon theory may open up
vast opportunities to compute dislocated materials at a full quantum many-body
level.
