Robots can locate odor sources in extreme conditions, such as underwater or in poisonous air, and work more effectively than animals while staying unharmed. Robotic odor source localization has grown in popularity over the past three decades. The majority of approaches proposed by researchers are categorized under four broad areas: bio or swarm-inspired methods, formation-based methods, probabilistic or infotaxis methods, and learning-based methods. In this work, we have included one more category that has recently been introduced in odor source localization. Further, we analyze the literature on these five categories and weigh their benefits and drawbacks. This study also addresses various odor source localization cases and examines the particular difficulties associated with each one. The significance of elements like environmental conditions and odor source modelling has also been analyzed. This review paper not only summarizes the state-of-the-art methods in odor source localization but also provides an analysis of their potential and limitations, offering insights into the challenges and opportunities for future advancements.