  Although inertial particle-laden flows occur in a wide range of industrial
and natural processes, there is both a lack of fundamental understanding of
these flows and continuum-level governing equations needed to predict transport
and particle distribution. Towards this effort, the Taylor-Couette flow (TCF)
system has been used recently to study the flow behavior of particle-laden
fluids under inertia. This article provides an overview of experimental,
theoretical, and computational work related to the TCF of neutrally buoyant
non-Brownian suspensions, with an emphasis on the effect of finite-sized
particles on the series of flow transitions and flow structures. Particles,
depending on their size and concentration, cause several significant deviations
from Newtonian fluid behavior, including shifting the Reynolds number
corresponding to transitions in flow structure and changing the possible
structures present in the flow. Furthermore, particles may also migrate
depending on the flow structure, leading to hysteretic effects that further
complicate the flow behavior. The current state of theoretical and
computational modeling efforts to describe the experimental observations is
discussed, and suggestions for potential future directions to improve the
fundamental understanding of inertial particle-laden flows are provided.
