I give a short non-technical review of the results obtained in recent work on
"Doubly Special Relativity", the relativistic theories in which the
rotation/boost transformations between inertial observers are characterized by
two observer-independent scales (the familiar velocity scale, c, and a new
observer-independent length/momentum scale, naturally identified with the
Planck length/momentum). I emphasize the aspects relevant for the search of a
solution to the cosmic-ray paradox.Comment: Invited piece for the N&V section of Nature. 5 pages, LaTe
