The Hopfield model represents a foundational paradigm in artificial intelligence, providing a prototypical example of an attractor neural network designed to implement associative memory. Since its introduction in the early 1980s as a biologically inspired model, it has been extensively studied by mathematicians and physicists alike. Its conceptual and scientific significance was further highlighted by the 2024 Nobel Prize in Physics awarded to John J. Hopfield. In this talk, I will review the main features of the Hopfield model as a spin-glass system through the framework of statistical mechanics of equilibrium. I will then present selected results from my research activity, focusing on the development of rigorous mathematical approaches to associative memories (including Guerra’s interpolation techniques and methods from random matrix theory) and highlighting connections between classical memory retrieval theory and contemporary machine-learning frameworks.