The growing number of mobile users with diverse applications such as VoIP, video, internet surfing etc. has made LTE networks to adopt a CAC strategy in order to ensure the quality of service (QoS) requirements of these applications. Over the years, several CAC schemes have been proposed to either accept or reject service requests. This paper presents a survey of these schemes under four different classes. The classes are: Bandwidth Reservation (BR), Bandwidth Degradation (BD), BR and BD and Non-BR and Non-BD (NBR-NBD). In each of the classification, the operation procedure, strengths and weaknesses of each scheme has been discussed. Furthermore, a comparative analysis of these schemes is also presented. The analysis provides insight into the challenges in the design of CAC by highlighting open research issues for future directions.