In a modern world, importance of computer modeling for solving complex engineering problems cannot be overstated. However, in a number of critical engineering problems computational models cannot provide unique answer and so further physical and analytical insight is required to guide computer simulations. Such an insight becomes even more valuable when off-nominal regimes of operation have to be considered. To deal with complexity of the physical process at the interface of multiple engineering systems a new discipline is emerging - operational physics of critical missions. This discipline combines an old-good physics based approach to modeling engineering problems with modern advanced technologies for analyzing continuous and discrete volving multiple modes of operation in uncertain environments, unknown state variables, heterogeneous software and hardware components. In this paper the new approach is illustrated using as an example analysis of the critical physics phenomena that lead to Challenger accident including physics of cryogenic explosion and propagation of detonation waves, internal ballistics of SRM's in the presence of the case breach fault, and monitoring of the structural integrity of the spacecraft.