  Initiated by Gromov, the study of holomorphic curves in symplectic manifolds
has been a powerfull tool in symplectic topology, however the moduli space of
holomorphic curves is often very difficult to find. A common technique is to
study the limiting behavior of holomorphic curves in a degenerating family of
complex structures which corresponds to a kind of adiabatic limit. The category
of exploded fibrations is an extension of the smooth category in which some of
these degenerations can be described as smooth families.
  The first part of this paper is devoted to defining exploded fibrations and a
slightly more specialized category of exploded torus fibrations. Later sections
contain the transverse interesction theory for exploded fibrations and some
examples of holomorphic curves in exploded torus fibrations, including a brief
discussion of the relationship between tropical geometry and exploded torus
fibrations. In the final section, the perturbation theory of holomorphic curves
in exploded torus fibrations is sketched.
