Driven class-B lasers are devices which possess quadratic nonlinearities and are known to exhibit chaotic behavior. We describe the onset of global heteroclinic connections which give rise to chaotic saddles. These form the precursor topology which creates both localized homoclinic chaos, as well as global mixed-mode heteroclinic chaos. To locate the relevant periodic orbits creating the precursor topology, approximate maps are derived using matched asymptotic expansions and subharmonic Melnikov theory. Locating the relevant unstable fixed points of the maps provides an organizing framework to understand the global dynamics and chaos exhibited by the laser.