  We explain how recent developments in the fields of realisability models for
linear logic -- or geometry of interaction -- and implicit computational
complexity can lead to a new approach of implicit computational complexity.
This semantic-based approach should apply uniformly to various computational
paradigms, and enable the use of new mathematical methods and tools to attack
problem in computational complexity. This paper provides the background,
motivations and perspectives of this complexity-through-realisability theory to
be developed, and illustrates it with recent results.
