Detonation waves in gases are very complex, involving a highly transient cellular structure and a turbulent reaction zone coupled with transverse shocks. The role of out-of-equilibrium phenomena in these waves remains unclear despite extensive research on the underlying physics. On the small scales, translational non-equilibrium associated with shocks, as postulated by Zel’dovich, may significantly affect the chemistry, and these effects are not yet fully understood. Similarly, very fast chemical processes may involve out-of-equilibrium effects due to local energy release that has been postulated by Prigogine. On larger scales, detonation waves display a cellular structure and are supported by turbulent combustion. The present thesis aims to quantify the importance of these three out-of-equilibrium effects on ignition, wave amplification, and diffraction limits of detonations. First, the role of translational non-equilibrium in reactive dynamics in the thermal explosion problem is investigated using molecular dynamics (MD) simulations and continuum models. Ignition delays are calculated and compared with rates from kinetic theory. MD results show agreement with the Prigogine and Mahieu corrections to the reaction rate evaluated from kinetic theory assuming a Maxwell-Boltzmann distribution. Accounting for the departure from translational equilibrium was found to reduce the ignition delay by up to 30% specifically at high activation energies. However, at low activation energies, the standard equilibrium rate shows a longer delay by up to 60%. The molecular dynamics simulations reveal that translational non-equilibrium effects accelerate activated exothermic reactions, referred to as “molecular hotspots”. The second part of the study focuses on the impact of thermal non-equilibrium and its coupling with reactive kinetics in shock-to-detonation transitions in gases. Results suggest that shock-induced ignition and transition to detonation involve non-equilibrium reactions that overlap with the shock structure, showing strong translational non-equilibrium with reactive fingers. Comparison with continuum simulations using different approximations reveals that shock amplification rate and transition to detonation are approximately twice as fast as predicted by conventional Euler hydrodynamic models, despite evidence of non-equilibrium. A Navier-Stokes model with hard sphere transport properties effectively captures the acceleration process, indicating significant implications for modeling gaseous detonations with fast reactions and strongly coupled pressure wave dynamics and reactivity in the detonation structure. In the last part of the thesis, the 3D hydrodynamic structure of cellular detonations is modeled by a global 1D mean hydrodynamic average model. Transport properties are artificially increased to account for the high-speed behavior resulting from fast turbulent diffusion. The existence of steady state Navier-Stokes detonation structure, as studied by Wood, is critically reviewed for this purpose and compared with transient calculations. Observations reveal that in the hyper-diffuse model, the shock and reaction zone overlap, resulting in a thickened reaction zone. The 1D model is used to study diffraction dynamics, with critical diffraction occurring when the tube diameter approaches the hydrodynamic reaction zone thickness. After diffraction, the complex viscous detonation structure separates, resulting in a rapid flame transitioning into a weak detonation. The conclusion of the present survey on the role of out-of-equilibrium effects on detonation dynamics suggests that non-equilibrium ignition due to molecular hotspots may give rise to corrections on the reaction rates by at most a factor of two. The coupling of exothermic reactions with the non-equilibrium structure of shock waves also predicts rates of shock amplification different by a factor of two from the standard Euler model for ignition, but accounting for the diffusive effects brings the MD and continuum predictions into closer agreement. Similarities with the out-of-equilibrium hydrodynamic structure of detonations are discussed.