Carbon nanotube fibers (CNTFs), the unidirectional macroscopic assembled structure of carbon nanotubes (CNTs), have excellent physicochemical properties including high tensile strength, flexibility, electrical conductivity, and thermal conductivity, which are desirable for utilizing the structural hexagonal graphitic structure ultimately. For last decades, to tailor their physical and chemical features of CNTFs, the research development on purification, spinning technique, and post processing have been pursued continuously. To outline the features of CNTFs, we first outlook the properties of single walled (SW), multi walled (MW) carbon nanotubes, as well as carbon fibers (CFs), which is helpful to predict what would be beneficial after assembling CNTs into fibers compared to CFs. Then we review the properties of single walled carbon nanotube fibers produced by several spinning techniques such as 1. vertically aligned CNT (VACNT) array spinning, 2. direct spinning from floating catalyst chemical vapor deposition (FCCVD), and 3. Wet spinning from CNT solution, together with the brief description of their production methods, respectively. At the end, we briefly describe their genuine and potential applications such as textile electronics, artificial muscles, energy storage devices, and automotive parts. We expect the understanding for CNTs and CNTFs are helpful for not only ensuring their practical use in aforementioned applications but also paving the way for the development of cutting-edge materials.