  We review the main concepts of the recently introduced principle of relative
locality and investigate some aspects of classical interactions between point
particles from this new perspective. We start with a physical motivation and
basic mathematical description of relative locality and review the treatment of
a system of classical point particles in this framework. We then examine one of
the unsolved problems of this picture, the apparent ambiguities in the
definition of momentum constraints caused by a non-commutative and/or
non-associative momentum addition rule. The gamma ray burst experiment is used
as an illustration. Finally, we use the formalism of relative locality to
reinterpret the well-known multiple point particle system coupled to 2+1
Einstein gravity, analyzing the geometry of its phase space and once again
referring to the gamma ray burst problem as an example.
