The possibility of producing complex metallic parts in various industries can be attributed to the selective laser melting (SLM) additive manufacturing method. As a powder bed fusion technique, SLM fabricates the product layer by layer. The state-of-the-art research on SLM, the metallic alloys utilized in the process, and the surface morphology of fabricated parts are discussed in this paper. The present report contributes to the literature by providing a comprehensive overview of the surface morphology of metallic alloys fabricated using the SLM additive manufacturing method. The article covers recent research on SLM, metallic alloys used in the process, and the surface morphology of fabricated parts. Insights into the challenges and opportunities of SLM for the fabrication of metallic parts with desired surface properties are provided. In the first part, parameters representing surface morphology are introduced and types of surface defects are viewed. Subsequently, influence of process variables during the production phase is discussed in-depth, overviewing several parameters such as laser, scanning, and geometric parameters. Surface morphology enhancement, namely in situ treatment, post-processing, and finishing-machining techniques, is viewed separately by classifying them into subtopics, in respect of their improvement effectiveness. Mechanical aspects of the microstructure and surface are evaluated in correlation with the surface morphology. The discussion of the findings considering the advantages and disadvantages of this technology is summarized finally. It is concluded that laser parameter effect’s significance depends on the work alloy. In the literature, process parameters are systematically studied, and better surface quality and favourable surface morphology of as build surfaces are possible. Moreover, it has been concluded that the surface morphology and quality of SLMed products can be improved with in situ techniques and post-treatments. Relieving residual stresses and decreasing porosity on the surface (various types of holes, pinholes, vacancies, etc.) during SLM operation are possible by base plate heating, powder preheating, and re-scanning. It is also noticed that the machinability studies of SLMed parts mainly focus on mechanical machining such as grinding and milling. Studies on the correlation between surface morphology of SLMed parts and mechanical properties are relatively scarce comparing to works on SLM production parameters. Finally, as an emerging technology for vast production of industrial items, it is concluded that surface morphology of SLMed products needs systematic correlation studies between process parameters and surface results.