Key points in the formation of liquid crystalline (LC) dispersions of graphene oxide (GO) and their processability via wet-spinning to produce long lengths of micrometer-dimensional fibers and yarns are addressed. Based on rheological and polarized optical microscopy investigations, a rational relation between GO sheet size and polydispersity, concentration, liquid crystallinity, and spinnability is proposed, leading to an understanding of lyotropic LC behavior and fiber spinnability. The knowledge gained from the straightforward formulation of LC GO "inks" in a range of processable concentrations enables the spinning of continuous conducting, strong, and robust fibers at concentrations as low as 0.075 wt%, eliminating the need for relatively concentrated spinning dope dispersions. The dilute LC GO dispersion is proven to be suitable for fiber spinning using a number of coagulation strategies, including non-solvent precipitation, dispersion destabilization, ionic cross-linking, and polyelectrolyte complexation. One-step continuous spinning of graphene fibers and yarns is introduced for the first time by in situ spinning of LC GO in basic coagulation baths (i.e., NaOH or KOH), eliminating the need for post-treatment processes. The thermal conductivity of these graphene fibers is found to be much higher than polycrystalline graphite and other types of 3D carbon based materials. New insights are provided into the processing of liquid crystalline graphene oxide (GO) dispersion (containing large GO sheets) demonstrating a facile and scalable production of GO and reduced GO fibers and yarns with exciting properties such as high thermal conductivity. These results provide a universal platform for the development of solution-based processing methods, properties, and applications of liquid crystalline GO-based architectures.