Machine type communication (MTC) is a fundamental technology to realize the concept of fully connected world in fifth generation (5G) Internet of Things (IoT). The massive roll out of the MTC devices is a serious challenge for cellular networks from operational and management perspective, including massive access and network congestion. Many proposals have been put forward by the research community to cater to the nuisance of massive MTC (mMTC) access in cellular networks. Recently, data aggregation has attracted a lot of research attention owing to its robust ability to resolve the above-mentioned challenges. In this paper, we review the recent development in data aggregation techniques, including their application scenarios, design, and limitations. Commencing with the application scenarios and current challenges in the MTC network, the classification of various proposed solutions for massive access along with the family of data aggregation techniques is discussed in detail. By doing so, it provides an insight about the future design trends that can propel the current research efforts to curb the mMTC access in a cellular network.