  Each approach to the quantum-gravity problem originates from expertise in one
or another area of theoretical physics. The particle-physics perspective
encourages one to attempt to reproduce in quantum gravity as much as possible
of the successes of the Standard Model of particle physics, and therefore, as
done in String Theory, the core features of quantum gravity are described in
terms of graviton-like exchange in a background classical spacetime. From the
general-relativity perspective it is natural to renounce to any reference to a
background spacetime, and to describe spacetime in a way that takes into
account the in-principle limitations of measurements. The Loop Quantum Gravity
approach and the approaches based on noncommutative geometry originate from
this general-relativity perspective. The condensed-matter perspective, which
has been adopted in a few recent quantum-gravity proposals, naturally leads to
scenarios in which some familiar properties of spacetime are only emergent,
just like, for example, some emergent collective degrees of freedom are
relevant to the description of certain physical systems only near a critical
point. Both from the general-relativity perspective and from the
condensed-matter perspective it is natural to explore the possibility that
quantum gravity might have significant implications for the fate of Lorentz
symmetry in the Planckian regime. From the particle-physics perspective there
is instead no obvious reason to renounce to exact Lorentz symmetry, although
(``spontaneous'') Lorentz symmetry breaking is of course possible. A
fast-growing phenomenological programme looking for Planck-scale departures
from Lorentz symmetry can contribute to this ongoing debate.
