A sliceform is a volumetric, honeycomb-like structure assembled from an array of cross-sectional planar slices that are interlocked via pairs of complementary slots placed along each intersection. If the slices are thin, these slotted intersections function as revolute joints, and the sliceform is foldable if the geometry of the embedded spatial linkage permits it, for example a lattice sliceform (LS) is bi-directionally flat-foldable. This thesis concerns a study of such sliceforms toward the design of novel deployable structures. A sliceform torus, composed of two sets of inclined slices arranged at regular intervals about a central axis of symmetry, has been discovered to exhibit a surprising and intriguing folding action whereby its incomplete form can be collapsed to a flat-folded stack of coplanar slices. On deployment, the assembly expands smoothly about an arc until the slices have rotated to their design inclination, then, without reaching any apparent physical limit, abruptly ‘locks out’. With a full complement of slices, the outermost intersections can be interlocked to complete and rigidify the ring. The torus is an example of a rotational sliceform (RS), and analysis of these structures proceeds by noting that their structural geometry comprises an array of pyramidal cells that is commensurate to a spherical scissor grid. The conditions for flat-foldability are determined by examination of the intrinsic geometry of each cell; the incompatibility of the slices with apparent rigid-folding revealed by assessment of the extrinsic motion of the slices. Investigation of their compliant kinematics reveals the articulation to be a bistable transition admitted by small transverse deflections of the slices. This structural form is generalised by development of a technique for generating sliceforms along a smooth spatial curve – curve sliceforms (CS). Their synthesis is more involved than for an RS, but a range of sliceform ‘tubes’ are generated and manufactured. Each example retains the flat-foldable, deployable characteristic of an RS, despite the apparent intrinsic rigidity of each constituent skew cell. Examination of the small-scale models indicates that deployable motion is achieved via imperfect action of the slots, and a simple model of the articulation of a single cell is constructed to investigate how this proceeds, verifying that motion is kinematically admissible via local deformations.