In-cylinder aero-thermal-chemical processes in reciprocating-piston internal combustion engines are rich and complex, and modern engines are already at high levels of refinement. Further increases in performance, reductions in fuel consumption and emissions, and accommodation for nontraditional fuels will require the effective use of high-spatial-and-temporal-resolution optical diagnostics and numerical simulations. CFD-based models must deal with mixed-mode turbulent combustion under largely unexplored thermochemical conditions, and must capture subtle influences of fuel composition on efficiency and emissions. For the models to be truly predictive, a proper accounting for the influences of unresolved turbulent fluctuations is required to capture complex interactions among hydrodynamic turbulence, gas-phase chemistry, dispersed liquid and/or solid phases (e.g., fuel sprays and/or soot) and radiation heat transfer. Transported probability density function (PDF) methods have emerged as one of the most promising and powerful frameworks for accommodating the effects of turbulent fluctuations in both Reynolds-averaged and large-eddy simulations. Within this framework, examples illustrating the importance of turbulence-chemistry-soot-radiation interactions (TCSRI) in laboratory flames and engines are presented and discussed. The ability of PDF-based models to accommodate realistic chemistry, detailed soot models, spectral radiation treatments and TCSRI is demonstrated.