Telecom networks are employed in numerous critical aspects of our society, such as business, financial services, and life-saving services. Natural disasters, misconfigurations, software upgrades, latent failures, and deliberate attacks can all cause several correlated failures in communication systems' physical infrastructures. These events may result in the long-term deterioration of telecommunications services. For this reason, research has to be carried out to know various methods used in designing survivability models used in resolving failures. A lot of research has been done on the review of telecom network failures, however, not sufficient work has been accomplished on the review of telecommunication network survivability. This paper presents a review and learning structure for telecommunication network survivability models to reveal hidden topics, which are less investigated. The survey comprises 119 accredited journal articles that have been published between 2001 and 2019 in 36 selected journals, which are suitable sources for telecommunication network failure survivability topics. The results reveal that there is a progressive volume of telecommunication network survivability models that have been carried out for various ranges of learning categories. The results reveal hidden telecommunication network survivability topics, which have received lesser attention. The findings can hopefully be used as a learning reference guide to understanding telecommunication network survivability models, as well as a source for researchers interested in telecommunication network survivability research to stimulate their further interests.