With exquisite precision and reproducibility, cells orchestrate the cooperative action of thousands of nanometer-sized molecular motors to carry out mechanical tasks at much larger length scales, such as cell motility, division and replication. Besides their biological importance, such inherently non-equilibrium processes are an inspiration for the development of soft materials with highly sought after biomimetic properties such as autonomous motility and self-healing. In this talk I will describe our exploration of such a class of biologically inspired active materials. Starting from extensile microtubule bundles, we hierarchically assemble active analogs of conventional polymer gels, liquid crystals and emulsions. At high enough concentration, microtubule bundles form an active gel network capable of generating internally driven chaotic flows that greatly enhance transport and fluid mixing. When confined to emulsion droplets, these 3D networks spontaneously adsorb onto the droplet surface to form a thin film of highly active 2D nematic liquid crystals whose streaming flows are controlled by internally generated cascades of fracture and self-healing, as well as unbinding and annihilation of oppositely charged disclination defects. The resulting active emulsions exhibit unanticipated emergent properties, such as autonomous motility driven by spontaneous unbinding of liquid-crystalline defects, which are unimaginable in their passive analogues. Taken together, these observations exemplify how assemblages of animate microscopic objects exhibit collective biomimetic properties that are starkly different from those found in materials assembled from inanimate building blocks, challenging us to develop a theoretical framework that would allow for a systematic engineering of their far-from-equilibrium material properties.