Reliable modeling of large-scale structures with the prediction of their durability is inevitably related to an adequate description of the used materials. Most of the building materials are heterogeneous with random morphology, which complicates namely the modeling of damage and application of traditional homogenization-based techniques. Therefore there are several strategies to handle this underlying material randomness within the context of structural simulations. This presentation is devoted to methods leading to the suitable characterization of the material properties based on different experimental observations, in other words, to methods solving different types of inverse problems. After the review and classification of selected inverse problems, the attention will be focused on material characterization by random fields constructed for two-phase and two-dimensional medium using the information extracted from its digital black-and-white image.