Multi-tenant service-based systems (SBSs) have emerged as a highly auspicious model within the contemporary cloud market, providing a variety of services tailored to meet the diverse requirements of multiple tenants through an assortment of service level agreement (SLA). Nevertheless, the intrinsic dynamic and interconnected nature of SBSs pose a threat of SLA breaches, potentially leading to an impending compromise in reliability. The identification of critical services (ICS) is vital when contemplating any suggested methods to improve reliability in SBS. A key benefit of ICS is reducing the number of component services that necessitate specific monitoring or redundancy actions. Reliability approaches, starting with ICS as a foundational stage, have been a prominent area of research interest since the 1990s. Over the years, researchers have devoted significant attention to ICS, especially within domains such as web services. This paper will examine a range of research works on ICS within SBS, particularly recent ones, focusing on criticality determined by Quality of Service (QoS) and tenant-specific criticality. The main goal is to differentiate between these facets and tackle the challenges and upcoming paths in this domain. Numerous challenges stem from the calculation of ICS, which can either be deterministic or stochastic. Furthermore, the lack of contextual factors concerning the variety of tenants or cloud service providers could present a hopeful opportunity. This paper offers an intriguing chance for researchers and developers to delve into within this domain, marking a forward stride in improving the reliability of SBS.