Massive machine-type communications (mMTC) is one of the key application scenarios of fifth generation (5G) and beyond cellular networks. Bringing the unique technical challenge of supporting a huge number of MTC devices (MTCD) in cellular networks, how to efficiently estimate the channel, detect the active users and data in this scenario is an open research topic. In this regard, this paper aims to present an overview of different techniques to address the problem of channel estimation, activity and data detection specifically for the mMTC scenario. In order to highlight potential solutions and to propose new research directions, we discuss the performance of the state-of-the-art techniques in the literature using a unified evaluation framework. INDEX TERMS 5G, channel estimation, detection, massive access, mMTC, random access.