The present review provides an overview of the current status and future perspectives of one of the smart manufacturing techniques of Industry 4.0, laser transmission welding (LTW) of semi-crystalline (SC) polymers and their composites. It is one of the most versatile techniques used to join polymeric components with varying thickness and configuration using a laser source. This article focuses on various parameters and phenomena such as inter-diffusion and microstructural changes that occur due to the laser interaction with SC polymers (specifically polypropylene). The effect of carbon black (size, shape, structure, thermal conductivity, dispersion, distribution, etc.) in the laser absorptive part and nucleating agent in the laser transmissive part and its processing conditions impacting the weld strength is discussed in detail. Among the laser parameters, laser power, scanning speed and clamping pressure are considered to be the most critical. This review also highlights innovative ideas such as incorporating metal as an absorber in the laser absorptive part, hybrid carbon black, dual clamping device, and an increasing number of scans and patterns. Finally, there is presented an overview of the essential characterisation techniques that help to determine the weld quality. This review demonstrates that LTW has excellent potential in polymer joining applications and the challenges including the cost-effectiveness, innovative ideas to provide state-of-the-art design and fabrication of complex products in a wide range of applications. This work will be of keen interest to other researchers and practitioners who are involved in the welding of polymers.