Numerical mantle convection models indicate that subducting slabs can reach the core-mantle boundary (CMB) for a wide range of assumed material properties and plate tectonic histories. An increase in lower mantle viscosity, a phase transition at 660 km depth, depth-dependent thermal expansivity, and depth-dependent thermal diffusivity do not preclude model slabs from reaching the CMB. We find that ancient slabs could be associated with lateral temperature anomalies ~500¿C cooler than ambient mantle. Plausible increases of thermal conductivity with depth will not cause slabs to diffuse away. Regional spherical models with actual plate evolutionary models show that slabs are unlikely to be continuous from the upper mantle to the CMB, even for radially simple mantle structures. The observation from tomography showing only a few continuous slab-like features from the surface to the CMB may be a result of complex plate kinematics, not mantle layering. There are important consequences of deeply penetrating slabs. Our models show that plumes preferentially develop on the edge of slabs. In areas on the CMB free of slabs, plume formation and eruption are expected to be frequent while the basal thermal boundary layer would be thin. However, in areas beneath slabs, the basal thermal boundary layer would be thicker and plume formation infrequent. Beneath slabs, a substantial amount of hot mantle can be trapped over long periods of time, leading to mega-plume formation. We predict that patches of low seismic velocity may be found beneath large-scale high seismic velocity structures at the core-mantle boundary. We find that the location, buoyancy, and geochemistry of mega-plumes will differ from those plumes forming at the edge of slabs. Various geophysical and geochemical implications of this finding are discussed.