  $^{229}$Th with a low-lying nuclear isomeric state is an essential candidate
for a nuclear clock as well as many other applications. Laser excitation of the
isomeric state has been a long-standing goal. With relativistic $^{229}$Th ions
in storage rings, high-power lasers with wavelengths in the visible range or
longer can be used to achieve high excitation rates of $^{229}$Th isomers. This
can be realized through direct resonant excitation, or excitation via an
intermediate nuclear or electronic state, facilitated by the tunability of both
the laser-beam and ion-bunch parameters. Unique opportunities are offered by
highly charged $^{229}$Th ions due to the nuclear-state mixing. The
significantly reduced isomeric-state lifetime corresponds to a much higher
excitation rate for direct resonant excitation. Importantly, we propose
electric dipole transitions changing both the electronic and nuclear states
that are opened by the nuclear hyperfine mixing. We suggest using them for
efficient isomer excitation in Li-like $^{229}$Th ions, via stimulated Raman
adiabatic passage or single-laser excitation. We also propose schemes for
probing the isomers, utilizing nuclear radiative decay or laser spectroscopy on
electronic transitions, through which the isomeric-state energy can be
determined with an orders-of-magnitude higher precision than the current value.
The schemes proposed here for $^{229}$Th could also be adapted to low-energy
nuclear states in other nuclei, such as $^{229}$Pa.
