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‎ Extensive efforts have been devoted to understanding brittle failure using numerical ‎simulation, as a complement to theory and experiments. In this thesis, peridynamic ‎models are used to study dynamic and quasi-static brittle fracture.‎ ‎ Failure in materials starts from the microscale and can affect, sometimes ‎catastrophically, the structure scale. The goal of computational modeling of fracture is to ‎predict the initiation, growth, and coalescence of cracks/damage. Achieving this goal ‎would allow one to change material design at the microstructure to increase toughness ‎and reliability. We first introduce a microstructure-level peridynamic model of solder ‎joints to understand fracture evolution under dynamic (drop-test) loading conditions. ‎Loads are transferred from the larger scale, for which we create a board-level finite ‎element analysis. We find that samples with larger inclusions show significantly more ‎cracks than those with smaller inclusions, which correlates well with experimental ‎observations. ‎ ‎ The approach mentioned above (explicit representation of material microscale) becomes ‎computationally prohibitive for problems in which the damage zone is relatively large, as ‎is the case of fiber-reinforced composites (FRC). Homogenization methods have been ‎well established for modeling the linear elastic behavior of FRCs, but not for fracture, a ‎nonlinear and dissipative phenomenon. Here we develop a fully-homogenized ‎peridynamic (FH-PD) model (using the Halpin-Tsai homogenization method) to simulate ‎transverse fracture of unidirectional FRCs. We show some limitations of this model and ‎introduce a new intermediately-homogenized peridynamic (IH-PD) model for transverse ‎loading of unidirectional FRCs. We show that the IH-PD model leads to crack path ‎tortuosity similar to that observed experimentally and without the need for an explicit ‎representation of the FRC microstructure.‎ ‎ For many decades, computational models have been over predict