Two-dimensional direct numerical simulations have been performed of the autoignition of (i) laminar and turbulent shearless mixing layers between fuel and hotter air, (ii) thin slabs of fuel exposed to air from both sides, and (iii) homogeneous stagnant adiabatic mixtures. It has been found that the time for the first appearance of an ignition site is almost independent of the turbulence time scale, varies little in individual realisations of the same flow, decreases with partial premixing, is shorter in turbulent than in laminar flows, and decreases with decreasing width of the fuel stream. The autoignition time in the turbulent flows is longer than the ignition delay time of stagnant homogeneous mixtures and this implies that the heat losses due to mixture fraction gradients associated with mixture inhomogeneities increase the autoignition time. It has also been found that ignition always occurs at a well-defined mixture fraction f(MR), which is accurately predicted by previous laminar flow analyses to depend only on the fuel and oxidant temperatures and the activation energy. As a measure of the heat losses of the heat-producing regions that eventually autoignite, the time evolution of the scalar dissipation rate, conditional on the most reactive mixture fraction, is examined and used to explain successfully all the observed trends of autoignition time with turbulent time scale, flow length scale, and partial premixing. The implications of these findings for modelling and for the interpretation of experimental data are discussed.