Our understanding of how magma-poor rifts accommodate strain remains limited largely due to sparse geophysical observations from these rift systems. To better understand magma-poor rifting processes, chapter 1 of this dissertation is focused on investigating the lithosphere-asthenosphere interactions beneath the Malawi Rift, a segment of the magma-poor Western Branch of the East African Rift (EAR). Chapter 2 and 3 are focused on investigating the sources of melt beneath the Rungwe Volcanic Province (RVP), an anomalous volcanic center located at the northern tip of the Malawi Rift. In chapter 1, we use the lithospheric structure of the Malawi Rift derived from the World Gravity Model 2012 to constrain three-dimensional (3D) numerical models of lithosphere-asthenosphere interactions, which indicate ~3 cm/yr asthenospheric upwelling beneath the thin lithosphere (115-125 km) of the northern Malawi Rift and the RVP from lithospheric modulated convection (LMC) that is decoupling from surface motions. We suggest that the asthenospheric upwelling may generate decompression melts which weakens the lithosphere thereby enabling extension. The source of asthenospheric melt for the RVP is still contentious. Some studies suggest the asthenospheric melt beneath the RVP arises from thermal perturbations in the upper mantle associated with plume head materials, while others propose decompression melting from upwelling asthenosphere due to LMC where the lithosphere is thin. Chapter 2 of this dissertation is focused on testing the hypothesis that asthenospheric melt feeding the RVP can be generated from LMC using realistic constraints on the mantle potential temperature (Tp). We develop a 3D thermomechanical model of LMC beneath the RVP and the entire Malawi Rift that incorporates melt generation. We find decompression melt associated with LMC upwelling (~3 cm/yr) occurs at a maximum depth of ~150 km localized beneath the RVP. Studies of volcanic rock samples from the RVP indicate plume signatures which are enigmatic since the RVP is highly localized, unlike the large igneous provinces in the Eastern Branch of the EAR. In chapter 3, we test the hypothesis that the melt beneath the RVP is generated from plume materials. We investigate melt generation from plume-lithosphere interactions (PLI) beneath the RVP by developing a 3D seismic tomography-based convection (TBC) model beneath the RVP. The seismic constraints indicate excess temperatures of ~250 K in the sublithospheric mantle beneath the RVP suggesting the presence of a plume. We find a relatively fast upwelling (~10 cm/yr) beneath the RVP which we interpret as a rising plume. The TBC upwelling generates decompression melt (~0.25 %) at a maximum depth of ~200 km beneath the RVP where the lithosphere is thinnest (~100 km). Our results demonstrate that an excess heat source from may be plume materials is necessary for melt generation in the sublithospheric mantle beneath the RVP because passive asthenospheric upwelling of ambient mantle will require a higher than normal Tp to generate melt. Studies of volcanic rock samples from the RVP indicate plume signatures which are enigmatic since the RVP is highly localized, unlike the large igneous provinces in the Eastern Branch of the EAR. In chapter 3, we test the hypothesis that the melt beneath the RVP is generated from plume materials. We investigate melt generation from plume-lithosphere interactions (PLI) beneath the RVP by developing a 3D seismic tomography-based convection (TBC) model beneath the RVP. The seismic constraints indicate excess temperatures of ≈ 250K in the sublithospheric mantle beneath the RVP suggesting the presence of a plume. We find a relatively fast upwelling (≈10 cm/yr) beneath the RVP which we interpret as a rising plume. The TBC upwelling generates decompression melt (≈0.25 %) at a maximum depth of ≈200 km beneath the RVP where the lithosphere is thinnest (≈100 km). Our results demonstrate that an excess heat source from may be plume materials is necessary for melt generation in the sublithospheric mantle beneath the RVP because passive asthenospheric upwelling of ambient mantle will require a higher than normal Tp to generate melt. / Doctor of Philosophy / Studies suggest the presence of hot, melted rock deep in the continents makes them weaker and easier to break apart, however, our understanding of how continents with less melted rock break apart remains limited largely due to sparse geophysical observations from these dry areas. To better understand how continents with less melted rock break apart, chapter 1 of this dissertation is focused on investigating the interactions between the rigid part of the Earth, called lithosphere, and the underlying lower viscosity rock layer called asthenosphere beneath the Malawi Rift, a segment of the magma-poor Western Branch of the East African Rift (EAR). Chapter 2 and 3 are focused on investigating the sources of melt beneath the Rungwe Volcanic Province (RVP), an anomalous volcanic center located at the northern tip of the Malawi Rift. In chapter 1, we use the lithospheric structure of the Malawi Rift derived from gravity data to constrain three-dimensional (3-D) numerical models of lithosphere-asthenosphere interactions, which indicate ~3 cm/yr asthenospheric upwelling beneath the thin lithosphere (115-125 km) of the northern Malawi Rift and the RVP that does not seem to drive movements at the surface. We suggest that the asthenospheric upwelling may generate melted rock which weakens the lithosphere thereby enabling extension. However, the source of asthenospheric melt for the RVP is still contentious. Some studies suggest the asthenospheric melt beneath the RVP arises from thermal perturbations in the upper mantle associated with rising mantle rocks or plume head materials, while others propose melting occurs from upwelling asthenosphere due to lithospheric modulated convection (LMC) where the lithosphere is thin. Chapter 2 of this dissertation is focused on testing the hypothesis that asthenospheric melt feeding the RVP can be generated from LMC. We develop a 3D thermomechanical model of LMC beneath the RVP and the entire Malawi Rift that incorporates melt generation. We find decompression melt associated with LMC upwelling (~3 cm/yr) occurs at a maximum depth of ~150 km localized beneath the RVP. Studies of volcanic rock samples from the RVP indicate plume signatures which are enigmatic since the RVP is highly localized, unlike the large igneous provinces in the Eastern Branch of the EAR. In chapter 3, we investigate melt generation from plume-lithosphere interactions (PLI) beneath the RVP. We develop a 3D model of convection using information from seismology we call tomography-based convection (TBC) beneath the RVP. The seismic data indicate excess temperatures of ~250 K beneath the RVP suggesting the presence of a plume. We find a relatively fast upwelling (~10 cm/yr) beneath the RVP which we interpret as a rising plume. The TBC upwelling generates decompression melt at a maximum depth of ~200 km beneath the RVP. Our results demonstrate that an excess heat source from may be plume materials is necessary for melt generation in the sublithospheric mantle beneath the RVP because passive asthenospheric upwelling of ambient mantle will require a higher than normal mantle potential temperatures to generate melt.