A comprehension of the complex dynamics of gaseous combustion requires an understanding of the underlying fundamentals. In this dissertation, I examine planar diffusion flames from both an experimental and numerical perspective. In the first part of this thesis, I study the extinction of unstrained, planar counter-diffusion flames. The theoretical model describing these flames was previously realized from experiments using the Porous Plug Counter-Diffusion (PPCD) burner. Using this burner, I conducted extinction experiments to determine the limiting extinction curves for propane-oxygen and methane-oxygen flames. The effects of burner configuration on extinction concentration are explored, comparisons between propane and methane are made, and the dependence of extinction concentration on mass flux is examined. In addition to the experimental work, the system was numerically modeled to compare the experimental work to model predictions. Also, using numerical simulations, it is shown that a simple chemistry model captures the essential behavior of the system as well as the more complex detailed chemistry model. Finally, the unstable behavior that was observed during the experiments is documented with comments as to the severity, types, and onsets of such behavior. In the second part of this thesis, I numerically simulate the effects of Lewis number on the propagation of circular extinction zones (flame holes). Analyzing the data from the numerical simulations leads to the discovery of a scaling law v = ar-b for the dependence of the hole collapse speed on the hole radius at any phase during the re-ignition (hole collapse) event on the flame sheet. Further observation shows that b depends solely on the dimensionless strain rate and is independent of the Lewis number. Also, it is found that decreasing the Lewis number increases the critical radius (i.e. the largest size of the hole that results in a re-ignition of the flame) for a given strain rate and that the scaling exponent of the critical radii with respect to strain rates is independent of the Lewis number. A better understanding of the effects of the Lewis number helps bridge the gap between analytic work where unity Lewis numbers are presupposed in many cases and the dynamics observed through experimentation. This leads to more accurate models of turbulent combustion and flame extinction. An improved understanding of colliding planar flames guides the more complicated problem of flame hole collapse and turbulence as well as having practical applications to various situations, such as in engine design.