A bluff-body has been employed as the flame stabilization scheme for many combustion devices such as gas turbines and aviation engines. Although the bluff-body flame holder has a key advantage of generating a hot gas recirculation zone behind it and assist in stable combustion, it also induces flow field and combustion instabilities such as unstable vortex shedding, which can adversely affect the flame stability and lead to blow-off. The understanding of the physical mechanism of flame stabilization and blow-off processes has been one of the critical subjects in premixed combustion systems under highly turbulent conditions. As considering this, the present dissertation presents insight of flame stabilization and blow-off mechanisms using several series of computational studies and detailed analysis using diagnostic approaches. Two-dimensional direct numerical simulations are conducted to examine flame/flow and blow-off dynamics in lean premixed hydrogen-air and syngas-air flames stabilized on a meso-scale bluff-body in a square channel. Several distinct effects on flame stabilization and blow-off dynamics are investigated, such as reduced confinement, hydrodynamic instability, flame time scale, and differential diffusion effects. For the analysis, a proper time scale analysis is attempted to characterize the flame blow-off mechanism, which turns out to be consistent with the classic blow-off theory of Zukoski and Marble. The combined approach of computational singular perturbation and tangential stretch rate is applied to examine chemical characteristics in blow-off dynamics. As an extension from Eulerian to Lagrangian viewpoint, Lagrangian particle tracking analysis of post-processing the pre-computed results is performed to examine the local characteristics during the critical transient event of local extinction and recovery.