Along with advancements in superconducting technology, especially in high temperature superconductors (HTS), the use of these materials in power system applications is gaining outstanding attention. Due to the lower weight, higher current carrying capability, and the lower loss of HTS cables compared to conventional counterparts, they are among the most focused applications of superconductors in power systems. In near future, these cables will be installed as key elements not only in power systems but also in cryo-electrified transportation units, which take advantage of both cryogenics and superconducting technology simultaneously, e.g. hydrogen-powered aircraft. Given the sensitivity of the reliable and continuous performance of HTS cables, any failures, caused by faults, could be catastrophic, if they are not designed appropriately. Thus, fault analysis of superconducting cables is crucial for ensuring their safety, reliability, and stability, and also for characterising the behaviour of HTS cables under fault currents at the design stage. Many investigations were conducted on the fault characterisation and analysis of HTS cables in the last few years. This paper aims to provide a topical review on all of these conducted studies, It will discuss the current challenges of HTS cables and after that current developments of fault behaviour of HTS cables would be presented, and then we will discuss the future trends and future challenges of superconducting cables regarding their fault performance.