  We review attempts to estimate the influence of global cosmological expansion
on local systems. Here `local' is taken to mean that the sizes of the
considered systems are much smaller than cosmologically relevant scales. For
example, such influences can affect orbital motions as well as configurations
of compact objects, like black holes. We also discuss how measurements based on
the exchange of electromagnetic signals of distances, velocities, etc. of
moving objects are influenced. As an application we compare orders of
magnitudes of such effects with the scale set by the apparently anomalous
acceleration of the Pioneer 10 and 11 spacecrafts, which is 10^-9 m/s^2. We
find no reason to believe that the latter is of cosmological origin. However,
the general problem of gaining a qualitative and quantitative understanding of
how the cosmological dynamics influences local systems remains challenging,
with only partial clues being so far provided by exact solutions to the field
equations of General Relativity.
