The effect of temperature on fuel-air ignition and combustion (thermal effects) have been widely studied and well understood. However, a comprehensive understanding of nonequilibrium plasma effects (in situ generation of reactive species and radicals combined with gas heating) on the combustion process is still lacking. Over the past decade, research efforts have advanced our knowledge of electron impact kinetics and low temperature chain branching in fuel-air mixtures considerably. In contrast to numerous experimental investigations, research on modeling and simulation of plasma assisted combustion has received less attention. There is a dire need for development of self-consistent numerical models for construction and validation of plasma chemistry mechanisms. High-fidelity numerical models can be invaluable in exploring the plasma effects on ignition and combustion in turbulent and high-speed flow environments, owing to the difficulty in performing spatially resolved quantitative measurements. In this work, we establish a multi-scale modeling framework to simulate the physical and chemical effects of nonequilibrium, nanosecond plasma discharges on reacting flows. The model is capable of resolving electric field transients and electron impact dynamics in sub-ns timescales, as well as calculating the cumulative effects of multiple discharge pulses over ms timescales. Detailed chemistry mechanisms are incorporated to provide deep insight into the plasma kinetic pathways. The modeling framework is utilized to study ignition of H₂-air mixtures subjected to pulsed, nanosecond dielectric barrier discharges in a plane-to-plane geometry. The key kinetic pathways responsible for radicals such as O, H and OH generation from nanosecond discharges over multiple voltage pulses (ns-ms timescales) are quantified. The relative contributions of plasma thermal and kinetic effects in the ignition process are presented. The plasma generated radicals trigger partial fuel oxidation and heat release when the temperature rises above 700 K, after which the process becomes self-sustaining leading to igntion. The ignition kernel growth is primarily due to local plasma chemistry effects rather than flame propagation, and heat transport does not play a significant role. The nanosecond pulse discharge plasma excitation resulted in nearly simultaneous ignition over a large volume, in sharp contrast to hot-spot igniters. Next, the effect of nanosecond pulsed plasma discharges on the ignition characteristics of nC₇H₁₆ and air in a plane-to-plane geometry is studied at a reduced pressure of 20.3 kPa. The plasma generated radicals initiate and significantly accelerate the H abstraction reaction from fuel molecules and trigger a “self-accelerating” feedback loop via low-temperature kinetic pathways. Application of only a few discharge pulses at the beginning reduces the initiation time of the first-stage temperature rise by a factor of 10. The plasma effect after the first stage is shown to be predominantly thermal. A novel plasma-flame modeling framework is developed to study the direct coupling of steady, laminar, low-pressure, premixed flames to highly non-equilibrium, nanosecond-pulsed plasma discharges. The simulations are performed with and without a burst of 200 nanosecond discharge pulses to quantify the effect of non-equilibrium plasma on a pre-existing lean premixed H₂/O₂/N₂ (ϕ = 0.5) flame at 25 torr. Simulation results showed a significant increase in O and H densities due to plasma chemistry, with peak values increasing by a factor of 6 and a factor of 4, respectively. It is demonstrated that Joule heating alone cannot move the temperature and species profiles as far upstream (i.e. closer to the burner surface) as the pulsed plasma source of the same total power. LES (large eddy simulation) of ignition and combustion of H₂ jets injected into a supersonic O₂ crossflow is performed. Nanosecond plasma discharges are studied for their potential to produce radicals and impact on the flame-holding process. The plasma has a significant effect on the O atom distribution near the discharge domain as well as in the leeward side of the second jet. The other species distributions, however, remained unchanged with or without plasma. We believe the reason for this behavior was the high jet momentum ratios considered in the present study. The plasma generated radicals were unable to have an effect on the flame development downstream because of the strong penetration of the cold fuel jet.