This Ph.D. thesis advances the fully coupling of robust shallow water flow and sediment transport modeling. The first part mainly focuses on the multislope MUSCL reconstruction for shallow water flow on unstructured grids. A limitation method for reconstruction of velocities avoids extremely high values for wet/dry fronts. The reconstruction methods are tested via analytical benchmarks and laboratory experiments and it has been shown that the MUSCL reconstruction at the middle point of the edge can obtain better results than the intersection point of the edge and the neighboring two cell centers. An improved vector manipulation method including more downwind information also provides more promising results than the original vector manipulation method based on the local value slopes. Further additional work related to a vector manipulation method considers a larger geometry stencil and more geometry relationships and through a straightforward implementation, a higher order accuracy and an increasing computational efficiency with increasing mesh size is obtained when compared to the previous work. In the second part, sediment movement is treated as additional transport source terms in the shallow water model and the coupled shallow water flow and sediment transport model is also discretized on unstructured grids using the aforementioned multislope MUSCL scheme of the first part to obtain high order accuracy. Regarding sediment transport, a bed load flux and a depth-averaged concentration flux sediment transport approach to be chosen depending on the flow conditions are compared. Sensitivity studies are carried out showing that Manning number and the sediment porosity are the most influencing parameters for bed load flux and depth-averaged concentration flux sediment transport model, respectively. Further development of the depth-averaged concentration flux model introduces the sediment velocity ratio to differentiate between the advection of the sediment and the advection of water. A modified Harten, Lax and van Leer Riemann solver with the contact wave restored (HLLC) is derived for the flux calculation based on the new wave pattern involving the sediment velocity ratio. The source term calculation is enhanced by means of a novel splitting-point implicit discretization. The slope effect is introduced by modifying the critical shear stress, with two treatments being discussed. The numerical scheme is tested in five examples that comprise both fixed and movable beds, model predictions show good agreement with measurements, except for cases where local three-dimensional effects dominate. Slope effect is further investigated by introducing the slope failure of the sediment assuming that a bed slide will occur if the bed slope exceeds a critical angle. This is enabled by means of a slope failure operator. Existing slope failure operators usually suffer from high computational costs and may fail at wet/dry fronts. Based on a modified mass balance approach, a novel slope failure operator for the total load transport model is developed. This slope operator is verified in three test cases, involving bank failure, dyke overtopping and a two-dimensional bank failure, and the numerical results from the proposed slope operator yield good agreement with analytical results and measurement data. In future work, real applications, parameter optimization, new slope failure operators and improved computational efficiency can be investigated.