Additive manufacturing, also known as 3D printing (3DP), is a novel and developing technology, which has a wide range of industrial and scientific applications. This technology has continuously progressed over the past several decades, with improvement in productivity, resolution of the printed features, achievement of more and more complex shapes and topographies, scalability of the printed components and devices, and discovery of new printing materials with multi-functional capabilities. Among these newly developed printing materials, carbon-nanotubes (CNT) based inks, with their remarkable mechanical, electrical, and thermal properties, have emerged as an extremely attractive option. Various formulae of CNT-based ink have been developed, including CNT-nano-particle inks, CNT–polymer inks, and CNT-based non-nanocomposite inks (i.e., CNT ink that is not in a form where CNT particles are suspended in a polymer matrix). Various types of sensors as well as soft and smart electronic devices with a multitude of applications have been fabricated with CNT-based inks by employing different 3DP methods including syringe printing (SP), aerosol-jet printing (AJP), fused deposition modeling (FDM), and stereolithography (SLA). Despite such progress, there is inadequate literature on the various fluid mechanics and colloidal science aspects associated with the printability and property-tunability of nanoparticulate inks, specifically CNT-based inks. This review article, therefore, will focus on the formulation, dispersion, and the associated fluid mechanics and the colloidal science of 3D printable CNT-based inks. This article will first focus on the different examples where 3DP has been employed for printing CNT-based inks for a multitude of applications. Following that, we shall highlight the various key fluid mechanics and colloidal science issues that are central and vital to printing with such inks. Finally, the article will point out the open existing challenges and scope of future work on this topic.