The needs of modern (additive) manufacturing (AM) technologies can no longer be satisfied by boundary representations (B-reps). AM requires the representation and manipulation of interior fields and materials. Further, while the need for a tight coupling between design and analysis has been recognized as crucial almost since geometric modelling (GM) has been conceived, contemporary GM systems only offer a loose link between the two, if at all. For more than half a century, the (trimmed) Non-Uniform Rational B-spline (NURBs) surface representation has been the B-rep of choice for virtually all the GM industry. Fundamentally, B-rep GM has evolved little during this period. In this talk, we seek to examine an extended, B-spline based, volumetric representation (V-rep) that successfully confronts the existing and anticipated design, analysis, and manufacturing foreseen challenges. We extend all fundamental B-rep GM operations, such as primitive and surface constructors, and Boolean operations, to trimmed trivariate V-reps. This enables the much-needed tight link between the designed geometry and (Isogeometric) analysis on one hand and the full support of (additive) manufacturing of porous, heterogeneous and anisotropic artifacts, on the other. Examples and applications of V-rep GM, that span design, analysis and optimization, and AM, of lattice- and micro-structure synthesis as well as heterogeneity, will also be demonstrated. ----------------------------------------------------------------------------- Work in collaboration with many others, including Ben Ezair, Fady Massarwi, Boris van Sosin, Jinesh Machchhar, Q Youn Hong, Sumita Dahiya, Annalisa Buffa, Giancarlo Sangalli, Pablo Antolin, Massimiliano Martinelli, Bob Haimes and Stefanie Elgeti.