In this talk, I will introduce our recent work on origami mechanisms and actuation strategies for applications spanning from biomedical devices to foldable space structures. The first topic is magnetically actuated millimeter-scale origami medical robots for effective amphibious locomotion in severely confined spaces or aqueous environments. The origami robots are based on the Kresling origami, whose thin shell structure 1) provides an internal cavity for drug storage, 2) permits torsion-induced contraction as a crawling mechanism and a pumping mechanism for controllable liquid medicine dispensing, 3) serves as propellers that spin for propulsion to swim, 4) offers anisotropic stiffness to overcome the large resistance from the severely confined spaces in biomedical environments. For the second part of my talk, the concept of hexagonal ring origami folding mechanism will be introduced as a strategy for deployable/foldable structures for space applications. The hexagonal rings can tessellate 2D/3D surfaces and each ring can snap to its stable folded configuration with only 10.6% of the initial area. Through finite-element analysis and the rod model, snap-folding of the hexagonal ring with slight geometric modification and residual strain are studied for easy folding of the ring to facilitate the design and actuation of hexagonal ring origami assemblies for functional foldable structures with extreme packing ratio.