  When chiral liquid crystals or magnets are subjected to applied fields or
other anisotropic environments, the competition between favored twist and
anisotropy leads to the formation of complex defect structures. In some cases,
the defects are skyrmions, which have 180{\deg} double twist going outward from
the center, and hence can pack together without singularities in the
orientational order. In other cases, the defects are merons, which have
90{\deg} double twist going outward from the center; packing such merons
requires singularities in the orientational order. In the liquid crystal
context, a lattice of merons is regarded as a blue phase. Here, we perform
theoretical and computational studies of skyrmions and merons in chiral liquid
crystals and magnets. Through these studies, we calculate the phase diagrams
for liquid crystals and magnets in terms of dimensionless ratios of energetic
parameters. We also predict the range of metastability for liquid crystal
skyrmions, and show that these skyrmions can move and interact as effective
particles. The results show how the properties of skyrmions and merons depend
on the vector or tensor nature of the order parameter.
