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This dissertation aims to use theory and numerical simulations to quantify the propagation of fronts, which consist of autocatalytic reaction fronts, fronts with feedback and pattern forming fronts in Rayleigh-Bénard convection. The velocity and geometry of fronts are quantified for fronts traveling through straight parallel convection rolls, spatiotemporally chaotic rolls, and weakly turbulent rolls. The front velocity is found to be dependent on the competing influence of the orientation of the convection rolls and the geometry of the wrinkled front interface which is quantified as a fractal having a non-integer box-counting dimension. Front induced solutal and thermal feedback to the convective flow field is then studied by solving an exothermic autocatalytic reaction where the products and the reactants can vary in density. A single self-organized fluid roll propagating with the front is created by the solutal feedback while a pair of propagating counterrotating convection rolls are formed due to heat release from the reaction. Depending on the relative change in density induced by the solutal and thermal feedback, cooperative and antagonistic feedback scenarios are quantified. It is found that front induced feedback enhances the front velocity and reactive mixing length and induces spatiotemporal oscillations in the front and fluid dynamics. Using perturbation expansions, a transition in symmetry and scaling behavior of the front and fluid dynamics for larger values of feedback is studied. The front velocity, flow structure, front geometry and reactive mixing length scales for a range of solutal and thermal feedback are quantified. Lastly, pattern forming fronts of convection rolls are studied and the wavelength and velocity selected by the front near the onset of convective instability are investigated. This research was partially supported by DARPA Grant No. HR0011-16-2-0033. The numerical computations were done using the resources of the Advanced Research Computing center at Virginia Tech.