Concepts that draw inspiration from soft biological tissues have enabled significant advances in creating artificial materials for a range of applications, such as dry adhesives, tissue engineering, biointegrated electronics, artificial muscles, and soft robots. Many biological tissues, represented by muscles, exhibit directionally dependent mechanical and electrical properties. However, equipping synthetic materials with tissue-like mechanical and electrical anisotropies remains challenging. Here, we present the bioinspired concepts, design principles, numerical modeling, and experimental demonstrations of soft elastomer composites with programmed mechanical and electrical anisotropies, as well as their integrations with active functionalities. Mechanically assembled, 3D structures of polyimide serve as skeletons to offer anisotropic, nonlinear mechanical properties, and crumpled conductive surfaces provide anisotropic electrical properties, which can be used to construct bioelectronic devices. Finite element analyses quantitatively capture the key aspects that govern mechanical anisotropies of elastomer composites, providing a powerful design tool. Incorporation of 3D skeletons of thermally responsive polycaprolactone into elastomer composites allows development of an active artificial material that can mimic adaptive mechanical behaviors of skeleton muscles at relaxation and contraction states. Furthermore, the fabrication process of anisotropic elastomer composites is compatible with dielectric elastomer actuators, indicating potential applications in humanoid artificial muscles and soft robots.