Solutions of carbon nanotubes (CNTs) in chlorosulfonic acid (CSA) form liquid crystals at high concentrations. From a fundamental perspective, CNTs are an ideal candidate system for testing theories of liquid crystals for rod-like systems with high degree of polydispersity. From an application perspective, these liquid crystal solutions are of special interest for the fluid-phase self-assembly approach for processing CNT-based macroscopic materials. Nevertheless, little is known about the morphology of the liquid crystal phase. Moreover, most of the literature on liquid crystals of CNTs has been focused on qualitative aspects of the phase behavior. In this thesis, we show that by using techniques including polarized optical microscopy and small angle x-ray scattering (SAXS), we can have a quantitative understanding of the ordering inside the liquid crystal phase and how it is affected by the CNT properties and the concentration. Polarized optical micrographs of the semi-dilute solutions of long CNTs show bi-continuous phases, while short CNTs show the formation of spindle- shaped nematic droplets (tactoids) emerging out of the isotropic phase. The unique shape of the nematic tactoids is a result of balancing between elastic and interfacial forces. The balance of these forces dictates that there must be a continuous transition in shape and director-field configuration that has eluded experiments for decades. We show that tactoids formed in solutions of CNTs in CSA present the first experimental observation of a continuous transition in shape and director-field configuration. We also show that the nematic liquid crystal droplets of CNTs in coexistence with the isotropic phase, partially wets the solid glass surface by forming flattened spindle- shaped sessile tactoids with non-constant contact angles. By measuring the shape of the droplets and coupling that to our theoretical predictions that is based on a macroscopic theory that incorporates the elastic response of the nematic phase in addition to various interfacial tensions, we developed the first method for characterizing the line tension in liquid crystal systems. Additionally, we show that SAXS can be used for CNT-CSA solutions to study the the ordering of the liquid crystal phase at high concentrations. Our studies on solutions of CNTs at high concentrations (~ 5 % by volume) reveal the formation of columnar phase at this concentration. Theoretically the nematic-columnar transition is expected to happen at higher concentrations (~ 50 % by volume) for rod-like systems. We attribute the early formation of the columnar phase to the steric forces rising from electrostatic forces between CNTs and thermal undulations of the individual CNTs.