Material fracture surrounds us every day from tearing off a piece of fresh bread to dropping a glass on the floor. Modeling this complex physical process has a near limitless breadth of applications in everything from computer graphics and VFX to virtual surgery and geomechanical modeling. Despite the ubiquity of material failure, it stands as a notoriously difficult phenomenon to simulate and has inspired numerous efforts from computer graphics researchers and mechanical engineers alike, resulting in a diverse set of approaches to modeling the underlying physics as well as discretizing the branching crack topology. However, most existing approaches focus on meshed methods such as FEM or BEM that require computationally intensive crack tracking and re-meshing procedures. Conversely, the Material Point Method (MPM) is a hybrid meshless approach that is ideal for modeling fracture due to its automatic support for arbitrarily large topological deformations, natural collision handling, and numerous successfully simulated continuum materials. In this work, we present a toolkit of augmented Material Point Methods for robustly and efficiently simulating material fracture both through damage modeling and through plastic softening/hardening. Our approaches are robust to a multitude of materials including those of varying structures (isotropic, transversely isotropic, orthotropic), fracture types (ductile, brittle), plastic yield surfaces, and constitutive models. The methods herein are applicable not only to the needs of computer graphics (efficiency and visual fidelity), but also to the engineering community where physical accuracy is key. Most notably, each approach has a unique set of parametric knobs available to artists and engineers alike that make them directly deployable in applications ranging from animated movie production to large-scale glacial calving simulation.