  In this survey, we remind some fibrations structure theorems (also called
Milnor's fibrations) recently proved in the real and complex case, in the local
and global settings. We give several Poincar\'e-Hopf type formulae which
relates the Euler-Poincar\'e characteristic of these fibers (also called
Milnor's fibers) and indices (topological degree) of appropriated vector fields
defined on spheres of radii small or big enough.
