A work on turbulent premixed combustion is timely because of increased concern about the environmental impact of combustion and the search for new combustion concepts and technologies. An improved understanding of lean fuel turbulent premixed flames must play a central role in the fundamental science of these new concepts. Lean premixed flames have the potential to offer ultra-low emission levels, but they are notoriously susceptible to combustion oscillations. Thus, sophisticated control measures are inevitably required. The editors' intent is to set out the modeling aspects in the field of turbulent premixed combustion. Good progress has been made recently on this topic. Thus, it is timely to edit a cohesive volume containing contributions from international experts on various subtopics of the lean premixed flame problem.