Digital electronics is a technological cornerstone in this modern society that has covered the increasing demand for computing power during the last decades thanks to a periodic doubling of transistor density in integrated circuits. Currently, such scaling law is reaching its fundamental limit, leading to the emergence of a large gamut of applications that cannot be supported by digital electronics, specifically, those that involve real‐time multi‐data processing, e.g., medical diagnostic imaging, robotic control, and autonomous driving, among others. In this scenario, an analog computing approach implemented in a real‐time reconfigurable nonelectronic hardware such as programmable integrated photonics (PIP) can be more efficient than digital electronics to perform these emerging applications. However, actual analog computing models such as quantum and neuromorphic computation were not conceived to extract the unique benefits of PIP (and integrated photonics in general). Here, the foundations of a new computation theory are presented, termed Analog Programmable‐Photonic Computation (APC), explicitly designed to unleash the full potential of PIP technology. Interestingly, APC enables overcoming basic theoretical and technological limitations of existing computational models and can be implemented in other technologies (e.g., in electronics, acoustics or using metamaterials), consequently exhibiting the potential to spark a ground‐breaking impact on the information society.