The optical domain presents potential avenues for enhancing both computing and communication due to its inherent properties of bandwidth, parallelism, and energy efficiency. This research focuses on harnessing 3-Dimensional (3D) diffractive optics for novel interconnect schemes as well as a nonlinear processing technique based on multiple scattering and representation of the input data multiple times. The initial discussion of this thesis revolves around the importance of 3D techniques for optical circuits. Transformations between 3D and 2D domains, vital in fields like optical tomography, additive manufacturing, and optical memory storage, are elaborated upon with a perspective of 3D optical circuit design. First, we use additive manufacturing at the micro-scale to create multilayered diffractive volume elements. The concept of Learning Tomography, which is a method to reconstruct 3D objects from 2D projections, is introduced as an inverse design approach to calculate these elements. Subsequently, we introduce the (3+1)D printing, a term we coined. This method facilitates the fabrication of graded-index optical devices, such as volume holograms and optical waveguides. A notable aspect of this technique is its capacity to produce volume holograms with a linear diffraction efficiency relation, breaking 1/M^2 limit. The research then examines the application of commercial spatial light modulators for constructing reconfigurable interconnect devices at a larger scale. By combining free space diffraction principles with repetitive wavefront shaping, we potentially offer enhanced connectivity between nodes in data center networks. The following section delves into the nonlinear characteristics found in opto-electronic systems where the optical part is solely linear. These nonlinearities are namely phase encoding, data detection, and multiple scattering. A theoretical framework is constructed for computing enabled by these transformations. We conclude by a multilayer diffractive optical network mimicking digital deep neural networks. The research posits that by utilizing multiple scattering with repetitive representation of the input data in the scattering potential, linear and nonlinear transformations can be achieved concurrently, which has significant implications for lowpower optical computing. In summary, this dissertation provides a comprehensive examination of current methodologies, tools, and challenges in the area of optical computing and interconnects, showcasing novel modalities, and suggesting directions for further research and development.