I will discuss how the concept of Fisher information provides a unifying framework for understanding the fundamental limits of optical measurements. When we infer properties of an object from scattered light, Fisher information quantifies how much can, in principle, be learned from the measurement, independently of any specific reconstruction algorithm. I will show how this viewpoint leads to practical strategies for improving optical experiments, including the use of wavefront shaping to actively maximise the information carried by scattered light. A particularly striking recent result is that Fisher information can be treated as a physical quantity that flows through space: its density and flux obey a continuity equation that closely mirrors the Poynting theorem for electromagnetic energy. This insight provides a powerful design principle for nanophotonic systems, enabling the deliberate routing and concentration of Fisher-information flow to enhance measurement precision. In the final part of the talk, I will briefly outline how these ideas extend beyond wave physics and how analogous notions of Fisher-information flow can be defined in artificial neural networks, offering a bridge between optical measurement theory and modern machine-learning methods.