  I briefly review some scenarios for the role of the Planck length in quantum
gravity. In particular, I examine the differences between the schemes in which
quantum gravity is expected to introduce a maximum acceleration and the schemes
in which the Planck length sets the minimum value of wavelengths (maximum value
of momentum). I also comment on some pictures for the structure of spacetime at
the Planck scale, such as spacetime discretization and spacetime
noncommutativity. I stress that some of these proposals can have significant
implications in astrophysics and cosmology.
