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The exponential growth of visual data, including 2D images and 3D modalities such as videos and multi-view images, has placed a premium on efficient representation and processing techniques that extend beyond traditional data compression. This thesis explores compression-driven approaches as innovative solutions for 2D and 3D vision, leveraging compression not merely for data reduction but as a transformative tool to enhance efficiency, versatility, and quality across various vision tasks. By leveraging the principles of compression, this thesis addresses a range of challenges, including reversible image transformations, learned lossy compression, joint task optimization with compression, as well as efficient 3D editing with compact yet expressive representations. To this end, we first develop frameworks that utilize invertible neural networks to encode and recover visual information with high fidelity, enabling tasks such as reversible image conversion and lossy image compression. By exploring the inherent invertibility of neural networks, we demonstrate that compression can serve as a reversible conduit for hiding and reconstructing multiple images within a single embedding, as well as improving the quality and efficiency of learned image compression codecs. We then extend image compression methods beyond data reduction by investigating their synergy with other tasks. Specifically, we propose a joint learning framework for image compression and denoising, leveraging the innate denoising capabilities of compression models. This approach achieves superior results in both domains while revealing the latent connections between data reduction and noise suppression. Finally, we expand the scope of compression to 3D vision, introducing a novel editing-friendly framework that encapsulates the appearance of 3D scenes into compact 2D canonical images. By treating the canonical image as a compressive representation of the 3D scene, this approach enables efficient 3D editing through standard 2D tools, eliminating the need for costly re-optimization while maintaining fidelity to the original scene.