This research project investigates the appropriateness of the cetane number (CN) as an index for Homogeneous Charge Compression Ignition (HCCI) combustion for numerous automotive fuels. Correlations between CN and HCCI auto-ignition are presented, followed by development of predictive models which describe the complex auto-ignition process. To this end, HCCI and PCCI combustion processes were studied from a fundamental perspective both experimentally and numerically: surrogate fuels with identical CN as the original fuels were characterized in an optically accessible Rapid Compression-Expansion Machine (RCEM) over a wide range of HCCI relevant engine conditions to provide an experimental database for model validation. The driving factors leading to ignition, as well as the resulting parameters of interest for HCCI combustion were identified, namely low and intermediate heat release, and ignition temperature. Two HCCI models were developed and extended for the surrogate fuels: I) a 3-Arrhenius model, suitable for ignition delay prediction and II) a model for the low temperature heat release (Cool-Flame model). New methodologies for model parameterization are presented which allow for model constant calibration of virtually any fuel. By combining the 3-Arrhenius and Cool-Flame models with a Livengood-Wu ignition integral, a fully predictive methodology for low and high temperature ignition delays was established, which can be used in both 0D- and 3D-simulations. The parameterized 0D model is validated for the surrogate data from the RCEM showing excellent agreement. When used in a 3D context, effects of flow-field, wall heat loss and stratification (temperature and mixture) can be accounted for. Predictions in the RCEM compare well to calculations using 3D-CFD with semi-detailed kinetics, at computational costs lower by several orders of magnitude. Towards PCCI combustion, two detailed numerical approaches (RANS-CMC and LES-CMC) were applied to study highly transient multiple injection combustion (ECN “Spray A”) for one diesel-like and one low temperature condition. Ignition delays and flame structures are predicted well and the results provide valuable insights w.r.t. the complex physical processes.