In the last decade, sensor, communication, and computing technologies have advanced rapidly, producing dramatic changes in our daily lives and in a variety of application domains. Emerging technologies are leading us to a gradual, but inescapable integration of our material and digital realities and the advent of cyber-physical worlds. Although attaining visual realism is within the grasp of current 3D modeling approaches, it is less clear whether current modeling techniques will accommodate the needs of human communication and of the applications that we can already envisage in those futuristic worlds. Inspired by the evolution trends of the Web, this article describes the evolution of shape modeling from the Shape 1.0 geometry-only, mesh-based stage to the forthcoming semantics-driven Shape 4.0 era.