Body Area Networks (BANs) are becoming increasingly popular and have shown great potential in real-time monitoring of the human body. With the promise of being cost-effective and unobtrusive and facilitating continuous monitoring, BANs have attracted a wide range of monitoring applications, including medical and healthcare, sports, and rehabilitation systems. Most of these applications are real time and life critical and require a strict guarantee of Quality of Service (QoS) in terms of timeliness, reliability, and so on. Recently, there has been a number of proposals describing diverse approaches or frameworks to achieve QoS in BANs (i.e., for different layers or tiers and different protocols). This survey put these individual efforts into perspective and presents a more holistic view of the area. In this regard, this article identifies a set of QoS requirements for BAN applications and shows how these requirements are linked in a three-tier BAN system and presents a comprehensive review of the existing proposals against those requirements. In addition, open research issues, challenges, and future research directions in achieving these QoS in BANs are highlighted.