Abstract: Cytoskeletal networks usually refer to cellular structures that are comprised of microtubules, actin filaments, intermediate filaments, and their associated accessory proteins and motor proteins, facilitating a range of cellular functions such as cell motion, division and growth. In addition to the narrow definition of “cytoskeleton” that provides frame support to an otherwise fluidic cell, cytoskeletal polymers play an important role in many other cellular functions. For example, bacteria flagella and spindle apparatus are essentially microtubules in different forms. In living cells, there are also hundreds of proteins and biochemical factors regulating the structure and dynamics of such networks, which makes it extremely difficult to elucidate the physical mechanisms behind these processes. In recent years, study of in vitro cytoskeletal polymer-motor protein networks built from purified protein components not only helps to understand the fundamental principles of non-equilibrium self-organization and dynamic behavior of cytoskeletal polymers and motor proteins on the subcellular level, but also sheds light on the design of active matter system and active machines that may operate far from equilibrium with life-like behaviors and functions. One notable success is the artificial active nematics built upon microtubules and kinesin motors, in which active stresses are used to generate macroscopic active flow and guide materials assembly. The active stress and order emergence of materials organization can also be tuned by a set of external parameters, such as external magnetic fields and light-activated proteins, in addition to the concentration of protein building blocks, ATP, and crowding agents. In this review, we focus on in vitro cytoskeleton-motor protein networks based on purified components including tubulin, actin, kinesin, and myosin, emphasizing on the non-equilibrium nature of microtubule and F-actin polymerization, generation of active stress and formation of dynamic networks, as well as the self-organization and dynamic behavior of subcellular structures on a larger scale. We conclude with the application of such networks in the study of active matter and artificial cells.