  Based on string theory, black hole physics, doubly special relativity and
some "thought" experiments, minimal distance and/or maximum momentum are
proposed. As alternatives to the generalized uncertainty principle (GUP), the
modified dispersion relation, the space noncommutativity, the Lorentz
invariance violation, and the quantum-gravity-induced birefringence effects are
summarized. The origin of minimal measurable quantities and the different GUP
approaches are reviewed and the corresponding observations are analysed. Bounds
on the GUP parameter are discussed and implemented in understanding recent
PLANCK observations on the cosmic inflation. The higher-order GUP approaches
predict minimal length uncertainty with and without maximum momenta.
