Wireless Sensor Networks (WSNs) are gaining popularity due to their low cost and ease of maintenance and management. One of the most challenging issues in WSN is energy conservation. The clustering strategy has the potential to extend the lifespan of WSNs. The selection of Cluster Head (CH) in each cluster is regarded as the capable approach for energy efficient routing in the clustering model, which reduces the transmission latency in the WSN. As a result, the routing method between nodes and sinks must take into account the efficient use of energy. In Low-Energy Adaptive Clustering Hierarchy (LEACH), direct data connection from source cluster head to sink is addressed, leading to inequitable energy consumption of cluster heads CHs and network routing gaps. In this paper, the conceptual framework of clustering in wireless sensor networks based on traditional and optimization categories is explored. In addition, the most relevant up-to-date researches in routing protocols are presented. The study presents a new taxonomy for categorizing current hierarchical energy efficiency routing protocols for WSNs and examines their functionality and performance. Next, the study examines current routing protocols in WSNs, ranging from traditional routing protocols to swarm intelligence-based protocols. LEACH variations are discussed using a taxonomy based on distinct classes, residual energy, centralization, distance, mobility, energy efficiency, and so on. The CH selection, hop count, mobility, scalability, energy efficiency, topology, and deployment are all compared in detail. Finally, Energy efficiency, data aggregation, location awareness, QoS, scalability, load balancing, fault tolerance, query based, and multipath are summarized for the hierarchical routing protocols that fall into both classes.