Mechanical metamaterials are emerging as an enabling technology for manipulating mechanical energy flow at will. The unique mechanical properties of these metamaterials are derived from structural architectures rather than their base materials. A natural question is how we design these architectures in a clever way to realize novel mechanical properties unprecedented in nature. In this presentation, I will talk about two powerful tools for designing mechanical metamaterials: origami and topology. First, I will show how origami design principle can be exploited to construct metamaterials that mitigate structural impact in an efficient way. Specifically, I will demonstrate a counter-intuitive mechanism of converting external compressive impact to tensile waves by using origami-based metamaterials. Second, I will talk about how the mathematical concept of topology can be applied to the design of mechanical waveguides. Inspired by the recent advent of topological insulators, I will show these topological waveguides can generate a defect-immune robust propagation of stress waves. Throughout the talk, I will place the experimental results in the context of potential engineering applications.