Optical imaging systems have evolved with the goal of producing an isomorphic measurement of a scene. Usually, such imaging systems place the sole burden of image formation on the optical front-end while the role of detector array is relegated to sampling and digitization of the optical image. Post-processing is typically viewed as a tool to mitigate image artifacts and noise, to apply compression and enable exploitation tasks such as pattern recognition, target tracking, etc. The traditional design approach optimizes each subsystem (optics, detector, post-processing) separately and often results in suboptimal designs. In contrast, computational optical imaging exploits the optical, detector and post-processing design degrees of freedom jointly to achieve end-to-end system optimality. Furthermore, such a design approach is especially suited to task-specific imaging as it allows one to incorporate knowledge of scene statistics and specific task in the system design. In this talk, I will discuss computational imaging system designs for two different tasks, image formation and pattern recognition, to illustrate the power of the joint-design framework. I will also talk about the emerging area of compressive imaging, where the number of measurement is much smaller than the inherent dimensionality of the scene, and its ability to significantly reduce the system's size, weight, power and cost. I will conclude by describing a task-specific information-theoretic approach to imaging system design and analysis in the context of fundamental limits of imaging systems.