  Time measured by an ideal clock crucially depends on the gravitational
potential and velocity of the clock according to general relativity.
Technological advances in manufacturing high-precision atomic clocks have
rapidly improved their accuracy and stability over the last decade that
approached the level of 10$^{-18}$. Based on a fully relativistic description
of the background gravitational physics, we discuss the impact of those
highly-precise clocks on the realization of reference frames and time scales
used in geodesy. We discuss the current definitions of basic geodetic concepts
and come to the conclusion that the advances in clocks and other metrological
technologies will soon require the re-definition of time scales or, at least,
clarification to ensure their continuity and consistent use in practice. The
relative frequency shift between two clocks is directly related to the
difference in the values of the gravity potential at the points of clock's
localization. According to general relativity the relative accuracy of clocks
in 10$^{-18}$ is equivalent to measuring the gravitational red shift effect
between two clocks with the height difference amounting to 1 cm. We show how
clock measurements can provide geopotential numbers for the realization of
gravity-field-related height systems and can resolve discrepancies in
classically-determined height systems as well as between national height
systems. Another application of clocks is the direct use of observed potential
differences for the improved recovery of regional gravity field solutions.
Finally, clock measurements for space-borne gravimetry are analyzed along with
closely-related deficiencies of this method like an extra-ordinary knowledge of
the spacecraft velocity, etc. For all these applications besides the
near-future prospects, we also discuss the challenges that are related to using
those novel clock data in geodesy.
