This chapter describes geometric strategies in origami design to create paper lanterns that gleam with the luminous gradations of light. While the design of origami paper lampshades is largely based on origami design, it also presents new challenges due to its specific set of design constraints as a new genre of functional art. This chapter intends to address this specific set of design constraints through understanding the underlying mathematics in origami design and provide a set of tools for constructing origami lampshade that results in high aesthetic quality. It begins with an introduction to origami design and its relationship to mathematics and the historical background on origami paper lanterns, it then discusses various geometric strategies for creating origami paper lampshades based on the Miura-ori, Yoshimura, and Waterbomb tessellations. The emphasis is on specific mathematical requirements for creating functional light art with dramatic and perceptual effects of translucent light.