Power systems are experiencing structural changes induced by the integration of distributed generation units and the operation of microgrids. This transformation has posed new challenges in well-established power system practices and especially on the design and coordination of protection systems. At roughly the same time, technological advancements in protective equipment have constituted the basis for the emergence of digital overcurrent relays which enable alternative approaches to standard protection schemes. As a consequence, recent studies aimed to provide a reliable protection system capable of responding to the modern power system conditions by propounding the utilization of non-standard characteristics (N-SCs), as opposed to the standard characteristics, i.e., characteristics that are not described in the currently used standards. Despite the fact that the effects of the aforementioned changes on the protection of power systems have been thoroughly analyzed in the technical literature, the requirements for devising N-SCs have not been discussed in detail so far. To address this gap, this paper classifies and analyzes the related studies with respect to their potential advantages and disadvantages. Moreover, based on the literature review, recommendations for further research in this area and a list of the requirements for devising robust non-standard relay characteristics are presented.