  The existence of neutron stars was not confirmed until the discovery of
pulsars at radio wavelengths in late 1960s. Since then, these highly compact
and magnetized objects have been observed across the electromagnetic spectrum,
and widely studied. However, lots of the studies related to neutron stars
require precise determination of their distances and proper motions. This
thesis focuses on high-precision astrometry of neutron stars using the data
from the Very Long Baseline Array (VLBA) and the Gaia space telescope
operating, respectively, at radio and optical frequencies. The neutron stars
studied in the thesis include the extremely magnetized magnetars, the
fast-spinning millisecond pulsars, the gravitational-wave-emitting double
neutron stars and neutron star X-ray binaries. As a major accomplishment, this
thesis presents the novel analysis and the results of the MSPSRpi project --
the largest astrometric survey of millisecond pulsars, then point out the
abundant implications of the astrometric results. Additionally, the release of
the astrometric results is bound to facilitate the detection of an
ultra-low-frequency gravitational-wave background. Methodologically, this
thesis applied advanced VLBI techniques to pulsar astrometry using the original
data reduction pipeline psrvlbireduce, which leads to the first two significant
magnetar parallaxes, and paves the way for studying magnetar formation channels
with their velocity distribution. The astrometry Bayesian inference package
sterne, developed during the PhD program, serves as a versatile and powerful
tool for the inference of astrometric parameters.
