IMS (IP Multimedia Subsystem) has become the basis of fixed-mobile convergence for telecommunication operators. Compared to previous networks, IMS presents huge advantages, especially in terms of its ability to offer all types of services (voice and data). Nevertheless, with these advantages comes a whole new package of resilience (dependability & security) challenge, e.g., attacks, human mistakes, large scale disasters, etc. In this paper, we provide an overview on the state of research in the field of IMS resilience. We propose a two-dimensional tree-based taxonomy of IMS resilience challenges. This taxonomy considers unique features of IMS such as the layered architecture. We also classify the existing countermeasures into eight classes. We identify the resilience objectives of these countermeasures and analyze their applicability and efficiency on challenge families.