  Active colloids in liquid crystals (ACLCs) is an active matter with
qualitatively new facets of behavior as compared to active matter that becomes
isotropic when relaxed into an equilibrium state. We discuss two classes of
ACLCs: (i) externally driven ACLCs, in which the motion of colloidal particles
is powered by an externally applied electric field, and (ii) internally driven
ACLCs, formed by self-propelled particles such as bacteria. The liquid crystal
(LC) medium is of a thermotropic type in the first case and lyotropic (water
based) in the second case. In the absence of external fields and self-propelled
particles, the ACLCs are inactive, with the equilibrium LC state exhibiting
long-range orientational order. The external electric field causes ACLCs of
type (i) to experience translations, rotations, and orbiting, powered by
mechanisms such as LC-enabled electrokinetics, Quincke rotations and entrapment
at the defects of LC order. A dense system of Quincke rotators, orbiting along
circularly shaped smectic defects, undergoes a transition into a collective
coherent orbiting when their activity increases. An example of internally
driven ACLCs of type (ii) is living liquid crystals, representing swimming
bacteria placed in an otherwise passive lyotropic chromonic LC. The LC strongly
affects many aspects of bacterial behavior, most notably by shaping their
trajectories. As the concentration of bacteria and their activity increase, the
orientational order of living liquid crystals experiences two-stage
instability: first, the uniform steady equilibrium director is replaced with a
periodic bend deformation, then, at higher activity, pairs of positive and
negative disclinations nucleate, separate, and annihilate in dynamic patterns
of topological turbulence. The ACLCs are contrasted to their isotropic
counterparts.

Soft Condensed Matter;Materials Science