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ISO 26262, titled Road Vehicles-Functional Safety, is the new automotive functional safety standard for passenger vehicle industry. In order to accomplish the goal of designing and developing dependable automotive systems, ISO 26262 uses the concept of Automotive Safety Integrity Levels (ASILs), the adaptation of Safety Integrity Levels. ASILs are allocated to the components and subsystems that can cause system failure and malfunctions that lead to hazards. ASILs allocation is a hard problem consists of finding the optimal allocation of safety levels to the system architecture which must guarantee that the highest safety requirements are met while development cost of the automotive system is kept minimum. There were many successful attempts to solve this problem using different techniques. However, it is worth pointing out that there is an absence of a review that provides an in-depth study of all the existing methods and highlights their merits and demerits. This paper presents an overview of different approaches that were used to solve ASILs allocation problem. The review provides an overview of safety requirements including the related standards followed by a study of the resolution methods of the existing approaches. The study of each approach provides a detailed explanation of the used methodology and a discussion of its strength and weaknesses including the main open challenges.