Through recent advances in modern production techniques, particularly in the field of additive manufacturing, new previously unthinkable geometries have become feasible. This vast realm of new possibilities cannot be adequately addressed by classical methods in engineering, which is why numerical design techniques are becoming more and more valuable. In this context, this work aims to present concepts that exploit the emerging possibilities and facilitate numerical optimization. The numerical optimization is built on a microstructured grid, where the geometry is constructed by means of functional composition between splines [1], resulting in a regular pattern of building blocks. Here, a macro-spline defines the outer contour, a micro-geometry sets the individual tiles and a parameter-spline controls the local parametrization of the microstructure, e.g., acting on the thickness or material density in a specific region [2]. This approach opens up a broad design space, where the adaptivity of the resulting microstructure can be easily extended by increasing the number of control variables in the parameters-spline via h- or p-refinement. The geometric representation uses volume splines, on the one hand providing full compatibility with CAD/CAM and on the other hand facilitating the use of Isogeometric Analysis (IGA). To fully utilize the potential of this type of geometry parameterization, gradient-based optimization algorithms are employed in combination with analytical derivatives of the geometry and adjoint methods. We will present first results in two fields of application, namely passive heat regulation and an elasticity problem. Here, we demonstrate how optimized microstructures can compensate for irregular boundary conditions and how compliance can be minimized using these lattice-like structures for major weight reduction. This research has been supported by European Union's Horizon 2020 research and innovation program under agreement No. 862025.