  Advancements in cosmology through next-generation ground-based gravitational
wave observatories will bring in a paradigm shift. We explore the pivotal role
that gravitational-wave standard sirens will play in inferring cosmological
parameters with next-generation observatories, not only achieving exquisite
precision but also opening up unprecedented redshifts. We examine the merits
and the systematic biases involved in gravitational-wave standard sirens
utilizing binary black holes, binary neutron stars, and neutron star-black hole
mergers. Further, we estimate the precision of bright sirens, golden dark
sirens, and spectral sirens for these binary coalescences and compare the
abilities of various next-generation observatories (A^sharp, Cosmic Explorer,
Einstein Telescope, and their possible networks). When combining different
sirens, we find sub-percent precision over more than 10 billion years of cosmic
evolution for the Hubble expansion rate $H(z)$. This work presents a broad view
of opportunities to precisely measure the cosmic expansion rate, decipher the
elusive dark energy and dark matter, and potentially discover new physics in
the uncharted Universe with next-generation gravitational-wave detectors.
