Shape-shifting materials from 2D thin sheets to 3D shapes are attractive for broad applications in programmable machines and robots, functional biomedical devices, and four-dimensional printing. Kirigami, the art of paper cutting, has recently emerged as a promising approach for shape morphing structures and materials due to its new properties such as auxeticity, stretchability, conformability, multistability, and optical chirality. In this talk, I will discuss our recent work in leveraging geometric designs of kirigami structures for programmable 3D morphologies and their applications in soft robotics. I will first talk about a general strategy motivated by the Gauss-Bonnet theorem utilizing the curvature of cut boundaries in kirigami sheets for target 3D curved morphologies through both forward and inverse designs. Then, I will discuss how to leverage programmable morphologies for nondestructive and delicate grasping and manipulating in soft robots. Finally, I will discuss two examples of harnessing tunable snapping capability and/or multistability yielded by the morphologies from geometric designs in soft robots.