Being able to design the microstructure of a material to achieve a desired macroscopic behavior is a key enabler for materials innovation. Achieving this goal requires detailed knowledge of how the local material structure influences effective mechanical properties such as stiffness, strength, or ductility. Ideally, experimental data and numerical simulations are combined to establish robust structure–property (SP) linkages. A central challenge then lies in inverting these linkages to identify microstructures that realize a prescribed set of target properties—an approach commonly referred to as inverse materials design. In this contribution, we employ stochastic descriptors to characterize complex microstructures across multiple length scales. Examples include volume fraction, generalized spatial n-point correlation functions, and Gram matrices derived from pre-trained convolutional neural networks. Corresponding statistically representative volume elements (SVEs) are generated using differentiable microstructure characterization and reconstruction (DMCR). Compared to other efficient reconstruction techniques, DMCR enables the prescription of generic, potentially high-dimensional microstructure descriptors, provided they are differentiable. The reconstructed microstructures are subsequently analyzed using numerical homogenization techniques to compute effective material properties, which are then combined with the microstructural descriptors to establish SP linkages. Since engineering data—particularly high-fidelity simulations and experiments—are generally costly to generate, inverse design must operate effectively in data-scarce regimes. We therefore investigate both direct and indirect inverse design strategies tailored to limited data availability. The presented methodology is demonstrated for two representative and complementary application domains: (i) spinodoid-based mechanical metamaterials, where complex yet smooth morphologies can be described using low-dimensional stochastic descriptors; and (ii) microstructures of secondary aluminum alloys contaminated by iron and silicon, where microstructural variability and defect populations critically affect mechanical performance. These examples highlight the versatility of the proposed framework for data-driven exploration of SP landscapes and inverse microstructure design in modern materials research.