This dissertation deals with the numerical investigation of the physics of sprays autoigniting at diesel engine conditions using Direct Numerical Simulations (DNS), and with the modelling of droplet related effects within the Conditional Moment Closure (CMC) method for turbulent non-premixed combustion. The dissertation can be split in four different sections, with the content of each being summarized below. The first part of the dissertation introduces the equations that govern the temporal and spatial evolution of a turbulent reacting flow, and provides an extensive review of the CMC method for both single and two-phase flows. The problem of modelling droplet related effects in the CMC transport equations is discussed in detail, and physically-sound models for the unclosed terms that appear in these equations and that are affected by the droplet presence are derived. The second part of the dissertation deals with the application of the CMC method to the numerical simulation of several n-heptane sprays igniting at conditions relevant to diesel engine combustion. Droplet-related terms in the CMC equations were closed with the models developed in the first part of the dissertation. For all conditions investigated, CMC could correctly capture the ignition, propagation and anchoring phases of the spray flame. Inclusion of droplet terms in the CMC equations had little influence on the numerical predictions, in line with the findings of other authors. The third part of the dissertation presents a DNS study on the autoignition of n-heptane sprays at high pressure / low temperature conditions. The analysis revealed that spray ignition occurs first in well-mixed locations with a specific value of the mixture fraction. Changes in the operating conditions (initial turbulence intensity of the background gas, global equivalence ratio in the spray region, initial droplet size distribution) affected spray ignition through changes in the mixture formation process. For each spray, a characteristic ignition delay time and a characteristic droplet evaporation time could be defined. The ratio between these time scales was suggested as a key parameter for controlling the ignition delay of the spray. The last part of the dissertation exploits the DNS simulations to perform an a priori analysis of the applicability of the CMC method to autoigniting sprays. The study revealed that standard models for the mixing quantities used in CMC provide poor approximations in two-phase flows, and are partially responsible for the poor prediction of the ignition delay time. It was also observed that first-order closure of the chemical source terms performs poorly during the onset of ignition, suggesting that second-order closures may be more appropriate for studying spray autoignition problems. The contribution of the work presented in this dissertation is to provides a detailed insight into the physics of spray autoignition at diesel engine conditions, to propose and derive original methods for incorporating droplet evaporation effects within CMC in a physically-sound manner, and to assess the applicability and shortcomings of the CMC method to autoigniting sprays.