  The different superfluid phases of $^3$He are described by $p$-wave order
parameters that include anisotropy axes both in the orbital and spin spaces.
The anisotropy axes characterize the broken symmetries in these macroscopically
coherent quantum many-body systems. The systems' free energy has several
degenerate minima for certain orientations of the anisotropy axes. As a result,
spatial variation of the order parameter between two such regions, settled in
different energy minima, forms a topological soliton. Such solitons can
terminate in the bulk liquid, where the termination line forms a vortex with
trapped circulation of mass and spin superfluid currents. Here we discuss
possible soliton-vortex structures based on the symmetry and topology arguments
and focus on the three structures observed in experiments: solitons bounded by
spin-mass vortices in the B phase, solitons bounded by half-quantum vortices in
the polar and polar-distorted A phases, and the composite defect formed by a
half-quantum vortex, soliton and the Kibble-Lazarides-Shafi wall in the
polar-distorted B phase. The observations are based on nuclear magnetic
resonance (NMR) techniques and are of three types: first, solitons can form a
potential well for trapped spin waves, observed as an extra peak in the NMR
spectrum at shifted frequency; second, they can increase the relaxation rate of
the NMR spin precession; lastly, the soliton can present the boundary
conditions for the anisotropy axes in bulk, modifying the bulk NMR signal.
Owing to solitons' prominent NMR signatures and the ability to manipulate their
structure with external magnetic field, solitons have become an important tool
for probing and controlling the structure and dynamics of superfluid $^3$He, in
particular half-quantum vortices with core-bound Majorana modes.
