In engineering, numerical methods have progressively evolved from tools for analysis and design into components of modern data-driven systems. The growing availability of distributed sensors, real-time data acquisition, and advances in machine learning are redefining this role, enabling computational models to learn from observations, incorporate prior physical knowledge, and adapt as new data become available. These capabilities are opening new paradigms in structural health monitoring, system identification, and adaptive design. At the same time, recent developments have demonstrated how computation can also emerge directly from the physical behavior of materials and structures, establishing a reciprocal relationship between mechanics and computation. These complementary perspectives can be framed as computing for mechanics, where computational tools support the analysis and design of mechanical systems, and mechanics for computing, where physical systems themselves perform computational tasks. Exploring the convergence of these directions may lead to a new paradigm in mechanics, inspired by spontaneous neurological processes such as learning and adaptation. Drawing on recent developments in structural optimization, structural health monitoring, and machine learning, this article discusses emerging trends at the interface between mechanics and computation, highlighting opportunities for structures capable of sensing, learning, and acting autonomously.