Session Initiation Protocol (SIP) is widely used as a signaling protocol to support voice and video communication in addition to other multimedia applications. However, it is vulnerable to several types of attacks because of its open nature and lack of a clear defense line against the increasing spectrum of security threats. Among these threats, flooding attack, known by its destructive impact, targets both of SIP User Agent Server (UAS) and User Agent Client (UAC), leading to a denial of service in Voice over IP applications. In particular, INVITE message is considered as one of the major root causes of flooding attacks in SIP. This is due to the fact that an attacker may send numerous INVITE requests without waiting for responses from the UAS or the proxy in order to exhaust their respective resources. Most of the devised solutions to cope with the flooding attack are either difficult to deploy in practice or require significant changes in the SIP servers implementation. Apart from these challenges, flooding attacks are much more diverse in nature, which makes the task of defeating them a real challenge. In this survey, we present a comprehensive study of flooding attack against SIP, by addressing its different variants and analyzing its consequences. We also classify the existing solutions according to the different flooding behaviors they are dealing with, their types, and targets. Moreover, we conduct a thorough investigation of the main strengths and weaknesses of these solutions and deeply analyze the underlying assumptions of each of them for better understanding of their limitations. Finally, we provide some recommendations for enhancing the effectiveness of the surveyed solutions and address some open challenges.