The development of advanced materials tailored for specific applications has become a cornerstone of modern engineering and science. In recent years, alongside the development of conventional materials with new properties, architected materials have come into focus. The macroscopic properties of such architected materials are determined not only by the base material itself but also by the arrangement of the base material on the mesoscale. The wide range of possible material structures provides additional design freedom for novel materials with customized properties. Naturally, this raises the question: How can structures be systematically identified that result in a specific target property of the architected material? This question can be approached in various ways. In this article, these approaches are categorized into direct and indirect inverse design, and a representative method from each category is presented. These two methods, tandem neural networks and Bayesian optimization, are applied to the inverse design of spinodoid architected materials for linear elastic properties and their effectiveness is demonstrated on individual examples.