Although many methods have been documented for carbon nanotube (CNT) synthesis, still, we notice many arguments, criticisms, and appeals for its optimization and process control. Industrial grade CNT production is urgent such that invention of novel methods and engineering principles for large-scale synthesis are needed. Here, we comprehensively review arc discharge (AD) and laser ablation (LA) methods with highlighted features for CNT production. We also display the growth mechanisms of CNT with reasonable grassroots knowledge to make the synthesis more efficient. We postulate the latest developments in engineering carbon feedstock, catalysts, and temperature cum other minor reaction parameters to optimize the CNT yield with desired diameter and chirality. The rate limiting steps of AD and LA are highlighted because of their direct role in tuning the growth process. Future roadmap towards the exploration of CNT synthesis methods is also outlined.