  According to a number of arguments in quantum gravity, both model-dependent
and model-independent, Heisenberg's uncertainty principle is modified when
approaching the Planck scale. This deformation is attributed to the existence
of a minimal length. The ensuing models have found entry into the literature
under the term Generalized Uncertainty Principle (GUP). In this work, we
discuss several conceptual shortcomings of the underlying framework and
critically review recent developments in the field. In particular, we touch
upon the issues of relativistic and field theoretical generalizations, the
classical limit and the application to composite systems. Furthermore, we
comment on subtleties involving the use of heuristic arguments instead of
explicit calculations. Finally, we present an extensive list of constraints on
the model parameter $\beta$, classifying them on the basis of the degree of
rigour in their derivation and reconsidering the ones subject to problems
associated with composites.
