Many macroscopic properties of materials are determined primarily by inhomogeneous structures and textures. These intermediate-scale structures often arise from competing interactions operating on different length scales within the material. Our understanding of such phenomena has increased substantially with the identification and theoretical description of solid-state materials with incommensurate and long-period modulated phases, such as ferroelectrics, charge-density-wave compounds, epitaxial layers and polytypes. Experimental diagnosis of inhomogeneous ground states and metastable phases...