The materials dealt with in this volume include wood, concrete, various metals, composites, ceramics, and porous geological media. Obviously, the properties and serviceability of such materials vary widely, and an almost universal theme in their testing is that the properties depend on the scale at which the analysis or observation is made. At each scale, "probability" plays an important role, where the word "probability" is used in a wider sense than the classical one. The book begins with a review of progress over recent years, identifying key questions that remain open. One point is how to observe/measure material properties at different scales, and whether a probabilistic approach, at each scale, is always applicable and advantageous. Obstacles to the identification of a universal approach include the wide range of materials and the diversity of applications. The hierarchical nature of materials and implications for modelling, testing and application are discussed extensively. Most contributions present both experimental and analytical/numerical results. A few are purely theoretical, and some are purely numerical.