  An overview on the various effects of axial symmetry breaking is presented
for medium heavy and heavy nuclei covering the mass number range 70 < A <240.
The discussion includes various observations for nuclei: level densities,
spectroscopic features as energies and transition rates, ground state masses
and finally the splitting of giant dipole resonances. Quadrupole moments and
rates can be derived from models of triaxial rigid rotation or cranking for a
given triaxiality parameters {\gamma}, but microscopic considerations are
needed to predict these for each nucleus investigated. Respective predictions
were made by recently made Hartree- Fock-Bogolyubov (HFB) calculations extended
to arbitrary triaxiality by a generator coordinate method. In accord to these,
various observations as reported in this overview demonstrate the importance of
allowing a breaking of axial symmetry for heavy nuclei already in the valley of
stability. Considering this breaking as indicated from the HFB approach
surprisingly many experimental data are well described globally without the
need for local fit parameters. In addition to these comparisons it will be
shown that it is advantageous to consider c{\gamma}=cos(3{\gamma}) an indicator
of axiality for heavy nuclei independent of their quadrupole moment.
