Hydrogen gas production using catalytic hydrocarbon cracking on metal nanoparticles has become a vital bridge technology, as this process, unlike the traditional methane-based reforming process, does not co-produce carbon gasses (e.g., CO, CO2). The major benefit of direct catalytic methane cracking using a nanostructured catalyst is the formation of solid carbon in high-value products, such as carbon nanotubes (CNTs) or filaments. This solid carbon can then be removed physically and valorized. However, it is challenging to design a catalyst capable of sustaining its activity after solid carbon has started to deposit and grow, meanwhile preventing the formation of coke. For CNTs, in particular, the base growth mode of CNTs is the desired pathway, as the catalyst can then be regenerated and re-used. If the CNTs are formed under the tip-growth mode, the catalyst particle will be lifted off the support of the regeneration and reusability is lost. Therefore, the study of CNTs growth modes is a vital topic, both experimentally and theoretically, of designing appropriate catalysts. To date, enormous efforts have been made to investigate conditions where the CNTs base growth mode can be maintained during the carbon deposition process. Several possible correlations and mechanisms regarding the base growth mode have been explored and established. Theoretical calculations and numerical simulations across length scales were conducted to investigate the nucleation mechanism and growth of CNTs. Density functional theory (DFT), classical and quantum-based molecular dynamics (MD) and Monte Carlo (MC) simulations were also carried out to study the initial CNT cap formation and its encapsulation during the catalytic hydrocarbon cracking process. A thermodynamics-based nucleation formula of CNTs for both the base and tip growth modes was also established. However, there is still no consensus on what determines the CNT growth modes and what the roles are of the various influencing factors such as the nanoparticle size, the oxidation state of the catalyst, the mechanical properties of CNT, and the catalyst-support interaction. This paper reviews the current status of CNT's growth mechanism development. The benefits and limitations of theory and modeling approaches concerning CNT growth modes are discussed.