The thermal and mechanical evolution of sediments in evolving extensional sedimentary basins represents a complex interaction of conductive, convective and advective processes. This thesis is concerned with the generation and dissipation of pressure via the movement of pore fluids driven by compaction, the advective flow of salt, and the thermal consequences of these processes on the maturation history of extensional basins. The flow of fluids is primarily controlled by the interactive properties between the fluids and the sediment framework, such as porosity, permeability, hydraulic conductivity and specific storage. These properties can be integrated in terms of a hydraulic diffusivity, which refers to the diffusion of pore pressure in porous sediments. When the pore pressure exceeds the hydrostatic pressure, the system is termed overpressured. If this overpressuring is developed within the sediments as they are deposited, then the system is both overpressured and undercompacted. Results of modeling using an inelastic compaction model for the behavior of the sediments to changes in pore pressure suggest that a hydraulic diffusivity minimum tends to develop within a basin at depths between 2 to 4 km and explains the depth to the top of overpressure observed in shale-dominated successions. Overpressured and undercompacted (i.e., anomalously high porosity) systems induce temperature anomalies within the undercompacted sediments and are a function of the low thermal conductivity and high heat capacity of the pore water with respect to sediment. The compaction and rheology of sediments control the large-scale heat transfer within basins. For inelastic compaction models, only overpressured and undercompacted systems can result in thermal anomalies in contrast to elastic compaction models where thermal anomalies are always associated with overpressure. When applied to the Gulf of Mexico basin, significant overpressure exists today within the Rio Grande and West Texas areas and was initiated since the Maastrichtian in response to the general west to east migration of sediment loads. Extreme overpressures are predicted to have occurred since the Miocene in response to the rapid progradation and sedimentation associated with the Mississippi delta system. The Gulf of Mexico is also characterized by the vertical and lateral advective flow of salt. In order to analyze the steady-state and transient thermal consequences of salt motion, flow patterns were emulated in terms of functions that are solutions of the Stokes equation but constrained by the observed geometries of the salt. Using this approach, it seems that the preservation of deep source rocks in the Gulf of Mexico is related to the ability of salt structures to act as heat "drains." Sediments below and in close proximity to the base of the salt are cooled significantly if the top of the structure is shallow (< 1000 m). Thus, the inclusion of salt and its associated geometries may induce a significant delay in the timing and level of maturation of subsalt source rocks.