  Quantum scale symmetry is the realization of scale invariance in a quantum
field theory. No parameters with dimension of length or mass are present in the
quantum effective action. Quantum scale symmetry is generated by quantum
fluctuations via the presence of fixed points for running couplings. As for any
global symmetry, the ground state or cosmological state may be scale invariant
or not. Spontaneous breaking of scale symmetry leads to massive particles and
predicts a massless Goldstone boson. A massless particle spectrum follows from
scale symmetry of the effective action only if the ground state is scale
symmetric. Approximate scale symmetry close to a fixed point leads to important
predictions for observations in various areas of fundamental physics.
  We review consequences of scale symmetry for particle physics, quantum
gravity and cosmology. For particle physics, scale symmetry is closely linked
to the tiny ratio between the Fermi scale of weak interactions and the Planck
scale for gravity. For quantum gravity, scale symmetry is associated to the
ultraviolet fixed point which allows for a non-perturbatively renormalizable
quantum field theory for all known interactions. The interplay between gravity
and particle physics at this fixed point permits to predict couplings of the
standard model or other "effective low energy models" for momenta below the
Planck mass. In particular, quantum gravity determines the ratio of Higgs boson
mass and top quark mass. In cosmology, approximate scale symmetry explains the
almost scale-invariant primordial fluctuation spectrum which is at the origin
of all structures in the universe. The pseudo-Goldstone boson of spontaneously
broken approximate scale symmetry may be responsible for dynamical dark energy
and a solution of the cosmological constant problem.
