Knowledge Graphs (KGs) have made a qualitative leap and effected a real revolution in knowledge representation. This is leveraged by the underlying structure of the KG which underpins a better comprehension, reasoning and interpretation of knowledge for both human and machine. Therefore, KGs continue to be used as the main means of tackling a plethora of real-life problems in various domains. However, there is no consensus in regard to a plausible and inclusive definition of a domain-specific KG. Further, in conjunction with several limitations and deficiencies, various domain-specific KG construction approaches are far from perfect. This survey is the first to offer a comprehensive definition of a domain-specific KG. Also, the paper presents a thorough review of the state-of-the-art approaches drawn from academic works relevant to seven domains of knowledge. An examination of current approaches reveals a range of limitations and deficiencies. At the same time, uncharted territories on the research map are highlighted to tackle extant issues in the literature and point to directions for future research.