During the previous few years, Wireless Sensor Network (WSN) appears as an active research domain due to the wide use of this technology in several applications, such as military, health, automation, and so forth. WSN supervises physical attributes where human activity is difficult or impossible. The WSN is a set of multiple sensor nodes that are haphazardly deployed in a specific space. These nodes sense data and record values continuously and send these data to the Base Station (BS) through other sensor nodes. Several issues are encountered in the WSNs, including energy consumption, deployment of sensor nodes, routing algorithms, energy efficiency, Cluster-Head (CH) selection, robustness, etc. Numerous routing protocols have been developed by researchers to resolve these constraints, and several techniques of optimization are proposed to define the optimal road between the transmitter and the receiving node. Hierarchical routing protocols increase the network lifetime by enhancing its performance. The most popular hierarchical method is LEACH (Low Energy Adaptive Clustering Hierarchy) that grouped sensor nodes into clusters. Each cluster consists of normal nodes and is controlled by a CH, which is elected by cluster members to collect their data and send it to the BS. The LEACH protocol decreased the energy consumption in WSNs. In this survey, we provide a comprehensive study of LEACH descendant clustering protocols. This survey is the first study to classify LEACH-based routing protocols into CH selection, data transmission, and both CH selection and data transmission techniques. This survey is compared to other actual surveys. To evaluate these protocols, we look at many metrics, such as the CH selection method, communication method, the scalability, energy efficiency, mobility, localization of nodes, and so forth. According to these metrics, we propose a comparative analysis of these clustering routing protocols. This survey discusses also the strengths and limitations of each LEACH-variant protocol. Conclusively, the paper terminates with recommendations on future research fields in WSN.