  Magnetic skyrmions are topologically stable nanoscale particle-like objects
that were discovered in 2009. Since that time, intense research interest has
led to the identification of numerous compounds that support skyrmions over a
range of conditions spanning cryogenic to room temperatures. Skyrmions can be
set into motion under various types of driving, and the combination of their
size, stability, and dynamics makes them ideal candidates for numerous
applications. Skyrmions represent a new class of system in which the energy
scales of the skyrmion-skyrmion interactions, sample disorder, temperature, and
drive can compete. A growing body of work indicates that the static and dynamic
states of skyrmions can be influenced strongly by pinning or disorder in the
sample; thus, an understanding of such effects is essential for the eventual
use of skyrmions in applications. In this article we review the current state
of knowledge regarding individual skyrmions and skyrmion assemblies interacting
with quenched disorder or pinning. We outline the microscopic mechanisms for
skyrmion pinning, including the repulsive and attractive interactions that can
arise from impurities, grain boundaries, or nanostructures. This is followed by
descriptions of depinning phenomena, sliding states over disorder, the effect
of pinning on the skyrmion Hall angle, the competition between thermal and
pinning effects, the control of skyrmion motion using ordered potential
landscapes such as one- or two-dimensional periodic asymmetric substrates, the
creation of skyrmion diodes, and skyrmion ratchet effects. We highlight the
distinctions arising from internal modes and the strong gyroscopic or Magnus
forces that cause the dynamical states of skyrmions to differ from those of
other systems with pinning. We also discuss future directions and open
questions related to the pinning and dynamics in skyrmion systems.
