Despite the exponential throughput improvement in mobile communications systems, their ability to satisfy requirements of stateof-the-art and future applications of advanced metering infrastructure (AMI) is still under investigation. Challenges are mainly due to the inadequacy of third generation partnership project (3GPP) networks to support large amounts of devices simultaneously, while the number of AMI end-devices and the frequency of their data transmission increase with new AMI-based applications. In this introductory survey, innovative and future AMI applications and their communication requirements are first reviewed. Then, we identify challenges of 3GPP long term evolution (LTE) in enabling future AMI applications. More importantly, the latest improvements to LTE-A standard release 12 and 13 are reviewed and analyzed with regards to their potential to improve the quality of LTE-enabled AMI. It is found that 3GPP enhancements on machine type communications (MTC) standards will significantly enhance AMI communications. Beyond MTC specifications, non-MTC-specific enhancements such as carrier aggregation and multi-connectivity for user equipment will also contribute greatly to improving reliability and availability of AMI devices. The paper's focus is towards improved backhaul support for innovative and future AMI applications, beyond traditional automatic meter reading.