Computational studies are performed on the autoignition and combustion characteristics encountered in modern internal combustion (IC) engines in which combustion is achieved primarily by autoignition of the reactant mixture. High-fidelity computational tools with varying levels of complexity are employed in order to systematically investigate the phenomena under consideration.;As a first baseline study, the effects of unsteady temperature fluctuations on the ignition of homogeneous hydrogen-air mixture in a constant-volume reactor is studied both computationally and theoretically using asymptotic analysis. It is found that ignition delay shows a harmonic response to the frequency of imposed temperature fluctuation and the response monotonically attenuates as frequency increases.;The effects of spatial transport on the autoignition characteristics are next investigated using a one-dimensional counterflow configuration, in which the well-defined unsteady scalar dissipation rate (chi) represents the effects of turbulent flow field. A newly defined ignitability parameter is proposed which systematically accounts for all the unsteady effects. n-Heptane, which exhibits a two-stage ignition behavior is studied next using similar configuration. Interestingly, two-stage ignition is observed even at significantly high initial temperatures when the ignition kernel is subjected to unsteady chi. Mechanism for the appearance of the two-stage ignition in unsteady conditions is found to be not chemical but is attributed to the spatial broadening of the ignition kernel and subsequent radical losses.;Guided by the above findings, multi-dimensional simulations are conducted to investigate the effects of spatial fluctuations in temperature and composition. Non-reacting 3D RANS engine simulations are first conducted to investigate different mixture formation scenarios that might exist in LTC engines prior to autoignition. Small-scale effects of these different mixture formation scenarios on the autoignition and subsequent front propagation are then studied using high-fidelity direct numerical simulation (DNS).;In the last part of dissertation, a novel principal component analysis (PCA) based approach is used to identify intrinsic low-dimensional manifolds in a complex autoigniting environment. A small number of principal components (PCs) are found to very well represent the complex reacting system. The approach thus provides a promising modeling strategy to reduce the computational complexity in solving realistic detailed chemistry in mixed-mode combustion systems.