Identifying the influential and spreader nodes in complex networks solves many types of complex scientific problems. In social networks, identifying the influential individuals can be useful for structuring techniques that accelerate or hinder information propagation. Each node in the network has unique characteristics that reflect its importance. These characteristics are used by researchers to design many different centrality algorithms. Unfortunately, current survey papers categorize these algorithms into broad classes and do not draw distinguishable boundaries among the specific techniques adopted by them. This can result in misclassifying unrelated algorithms into the same analysis category. To overcome this, we introduce a methodology-based taxonomy for classifying the algorithms that identify top-k influential spreaders into hierarchically nested, specific, and fine-grained categories. We survey 184 papers and discuss their algorithms, which fall under 26 specific techniques. Our methodological taxonomy classifies the algorithms hierarchically into the following manner: Analysis type analysis scope analysis approach analysis category analysis sub-category analysis specific technique. We introduce in this paper a comprehensive survey, review, and experimental evaluation of the recent and state-of-the-art algorithms that identify the top-k and influential spreader nodes in social networks.