In the field of optimal structural design, topology optimization has been shown to be one of the most powerful methodologies. For a given domain under known loading conditions, topology optimization seeks to find the layout of material that optimizes a performance metric. Much of the work on topology optimization had concerned elasticity. This limits its real-world use in applications such as impact resistance, which require: plasticity, three-dimensional solid mechanics, transient dynamics, and material failure. We present a gradient-based topology optimization formulation for a plastic continuum solid and explore results for a model canonical problem. This naturally leads to the extension of damage and material failure.