Nature provides awe-inspiring lessons in designing materials structures from simple building blocks to achieve necessary performance.  In these designs, ubiquitous forces are utilized to impart control of both structure and performance.  For example, forces associated with differential growth lead to the formation of complex structures, such as fingerprints.  Likewise, van der Waals and capillary forces are used by geckos to achieve a unique balance of adhesion and locomotion through a differentiated hierarchy in their foot structure.  Here, we present an overview of efforts within our group to learn from Nature in the design of materials and in concepts that lead to fundamental understanding of materials.  First, we describe how the same balance of materials properties and geometry that control draping in a thin film can be advantageous for the hierarchical design of reversible, elastomer-based adhesives.  Second, we describe how elastic instabilities in elastomers, such as wrinkling and folding, can be used systematically to define surface structures with discretized length scales. These stories, as well as other highlights, demonstrate how important lessons from Nature can be utilized to impact the design and fabrication of materials structures for a wide range of technologies.