We propose a flexible light-field camera architecture that represents a convergence of optics, sensor electronics, and applied mathematics. Through the co-design of a sensor that comprises tailored, angle-sensitive pixels and advanced reconstruction algorithms, we show that, contrary to light-field cameras today, our system can use the same measurements captured in a single sensor image to recover either a high-resolution 2D image, a low-resolution 4D light field using fast, linear processing, or a high-resolution light field using sparsity-constrained optimization.