When designing materials for a given property, it is often easier to pick periodic structures, as periodicity greatly facilitates the analytical predictions and numerical simulations of the expected behavior of the system. However, some properties are only achievable in aperiodic, or even disordered materials. In such materials, many difficulties arise -- in particular, it is not always clear which structural signature is responsible for a given property. It is thus highly desirable to have a platform to easily and quickly generate candidate structures with well-controlled correlations, to then test their properties systematically. In this talk, I will start by presenting the Fast Reciprocal-Space Correlator (FReSCo), an algorithm designed to enforce pair correlations in point patterns with the best possible computational performance. I will highlight that it can be used for fast generation of large systems of interest, like hyperuniform systems, or for materials discovery, with the example of gyromorphs. Then, I will present extensions of the method in 2 directions: optimization in non-flat space, and the optimization of higher-order correlations. I will discuss how these extensions open up exciting perspectives in materials discovery, the elucidation of the structure-function relationship in disordered systems, and signal processing.