Over the past decade, entanglement of curvilinear cylinders in space have attracted significant interest in the chemical sciences, particularly in the study of metal-organic and covalent-organic frameworks. as the synthesis of increasingly complex structures becomes possible. In this talk, we will explore two classes of entangled materials and develop geometric models to describe them. The first part introduces a robust geometric model for triply periodic cylinder packings based on the orthogonal clasp. A special class of chiral cylinder packings exhibits a cooperative unwinding mechanism akin to auxeticity — an expansive lateral response when stretched in a fixed direction. This unique property makes such structures highly promising for the design of metamaterials with targeted functionalities, including impact protection and filtration. In the second part, we extend the theory of planar weavings to curved surfaces to model polyhedral entanglements. A subclass of polycatenanes has already been synthesized by chemists using metal-peptide rings. By constructing a tensegrity-based framework to analyze weavings in curved space, we model curved weavings as a nonlinear optimization problem. Our model works particuilarly well on surfaces where all points are geometrically identical, accurately describing the behavior of weavings on both the sphere and the flat torus. To identify the weave that energetically favors the sphere most, we deform the underlying surface into a spheroid. An analysis of the associated energy landscape of this deformation reveals that the more regular the weave, the more it prefers the sphere.