Internet is becoming the infrastructure and starts to carry more critical mission traffic where even a short disruption can cause significant losses for certain applications. Nevertheless, traditional route protocols have the problem of long convergence delay, transient unreachability and loop upon the network topology changes due to links/nodes failure or various other reasons. Unfortunately, the transient routing failures are very common according to the experimental studies. Numerous routing protocols which can provide disruption-free forwarding and fast recovery have been proposed. This paper firstly studies the root cause of transient failures, and then presents classification standards for survivable routing protocols. Thereafter, it focuses on analyzing the fundamental mechanism of existing representative survivable routing protocols and comparing their characteristics, performance and overhead. Finally, the current research status and open research issues are concluded.