  The low-energy, long-lived isomer in $^{229}$Th, first studied in the 1970s
as an exotic feature in nuclear physics, continues to inspire a
multidisciplinary community of physicists. Using the nuclear resonance
frequency, determined by the strong and electromagnetic interactions inside the
nucleus, it is possible to build a highly precise nuclear clock that will be
fundamentally different from all other atomic clocks based on resonant
frequencies of the electron shell. The nuclear clock will open opportunities
for highly sensitive tests of fundamental principles of physics, particularly
in searches for violations of Einstein's equivalence principle and for new
particles and interactions beyond the standard model. It has been proposed to
use the nuclear clock to search for variations of the electromagnetic and
strong coupling constants and for dark matter searches.
  The $^{229}$Th nuclear optical clock still represents a major challenge in
view of the tremendous gap of nearly 17 orders of magnitude between the present
uncertainty in the nuclear transition frequency and the natural linewidth.
Significant experimental progress has been achieved in recent years, which will
be briefly reviewed. Moreover, a research strategy will be outlined to
consolidate our present knowledge about essential $^{229\rm{m}}$Th properties,
to determine the nuclear transition frequency with laser spectroscopic
precision, realize different types of nuclear clocks and apply them in
precision frequency comparisons with optical atomic clocks to test fundamental
physics. Two avenues will be discussed: laser-cooled trapped $^{229}$Th ions
that allow experiments with complete control on the nucleus-electron
interaction and minimal systematic frequency shifts, and Th-doped solids
enabling experiments at high particle number and in different electronic
environments.
