Wireless body area sensor network is a special purpose wireless sensor network that, employing wireless sensor nodes in, on, or around the human body, makes it possible to measure biological parameters of a person for specific applications. One of the most fundamental concerns in wireless body sensor networks is accurate routing in order to send data promptly and properly, and therefore overcome some of the challenges. Routing protocols for such networks are affected by a large number of factors including energy, topology, temperature, posture, the radio range of sensors, and appropriate quality of service in sensor nodes. Since energy is highly important in wireless body area sensor networks, and increasing the network lifetime results in benefiting greatly from sensor capabilities, improving routing performance with reduced energy consumption presents a major challenge. This paper aims to study wireless body area sensor networks and the related routing methods. It also presents a thorough, comprehensive review of routing methods in wireless body area sensor networks from the perspective of energy. Furthermore, different routing methods affecting the parameter of energy will be classified and compared according to their advantages and disadvantages. In this paper, fundamental concepts of wireless body area sensor networks are provided, and then the advantages and disadvantages of these networks are investigated. Since one of the most fundamental issues in wireless body sensor networks is to perform routing so as to transmit data precisely and promptly, we discuss the same issue. As a result, we propose a classification of the available relevant literature with respect to the key challenge of energy in the routing process. With this end in view, all important papers published between 2000 and 2015 are classified under eight categories including ‘Mobility-Aware’, ‘Thermal-Aware’, ‘Restriction of Location and Number of Relays’, ‘Link-aware’, ‘Cluster- and Tree-Based’, ‘Cross-Layer’, ‘Opportunistic’, and ‘Medium Access Control’. We, then, provide a full description of the statistical analysis of each category in relation to all papers, current hybrid protocols, and the type of simulators used in each paper. Next, we analyze the distribution of papers in each category during various years. Moreover, for each category, the advantages and disadvantages as well as the number of issued papers in different years are given. We also analyze the type of layer and deployment of mathematical models or algorithmic techniques in each category. Finally, after introducing certain important protocols for each category, the goals, advantages, and disadvantages of the protocols are discussed and compared with each other.