Combustion remains one of the most challenging subject, which combines the extreme intricacies of chemical reactions at nanoscales with a large variety of macroscale phenomena such as flow vortices. For a typical application like a gas turbine or rocket engine, the timescales and lengthscales vary by well over ten orders of magnitudes. It is therefore no surprise that our understanding of combustion lags far behind applications, a situation that is similar to biology (we know our brains work but don’t why or how to control). One of the most powerful tools to further our understanding is direct numerical simulation (DNS), which aims to solve the governing equations of combustion without modelling uncertainties. The development of DNS is closely related to advancement in computing technologies. Over the past two decades, computers at the high end increased from megaflops to petaflops, which has greatly expanded the usefulness of combustion DNS and accelerated our understanding of turbulent combustion. The talks will review these advances in the worldwide context (but inevitably from a personal perspective and with a UK focus). Examples will be shown to demonstrate the capabilities of DNS for both gas and multiphase turbulent combustion. The potentials, limitations and future developments of combustion DNS will be discussed.