Combustion environments in propulsion systems involve the interaction of a variety of physics. In devices such as augmentors, ramjets and scramjets, such environments include the interaction between combustion, high-intensity turbulence, and/or strong flow compressions and expansions, physics which are termed here high-speed combustion. With this motivation in mind, this paper addresses: What are the problems encountered when modeling these interactions, or in other words, what are the problems of turbulent-combustion modeling? Do such interactions need modeling? What are the challenges when going from modeling low-speed- to high-speed-combustion problems? This work addresses these questions by summarizing several modeling studies of gaseous high-speed-combustion problems, and attempts to interpret some predictions in the context of the models' basic assumptions. Interestingly, the challenges to model high-speed combustion are such that a reader not interested in this topic but in the general one of modeling turbulent combustion may find the present paper useful. (C) 2017 Published by Elsevier Ltd.