As the number of framework materials known and characterized in the literature grows, it becomes apparent that they can carry properties rarely encountered in more conventional, dense inorganic materials. Among these materials with unusual physical or chemical properties are the ubiquitous metal-organic frameworks, covalent organic frameworks, dense coordination polymers, and molecular frameworks. Many can respond to stimulation by displaying structural responses and changes in properties that range from counter-intuitive to thermodynamically forbidden. In that, they share large similarities with metamaterials, which are engineered to generate properties not found in “normal” materials. We review here the surprising behavior of these meta-MOFs and other framework materials that display properties “beyond” (μετά) the boundaries of common crystalline materials.