We propose a novel approach to embed the physics-informed machine learning paradigm into the framework of Isogeometric Analysis (IGA) to combine the best of both worlds. In contrast to other learning-based approaches, which predict point-wise solution values, IgaNets learn solutions in terms of their expansion coefficients relative to a given B-Spline or NURBS basis. This approach is furthermore used to encode the geometry and other problem parameters such as boundary conditions and parameters of the constitutive laws and feed them into the network as inputs. Once trained, IgaNets enable exploring various designs from a family of similar problem configurations efficiently without the need to perform a computationally expensive simulation for each new problem configuration. Next to discussing the IgANets concept and possible applications within additive manufacturing, we will demonstrate an interactive and collaborative design-through-analysis workflows.