Massive machine-type communication (mMTC) and ultra-reliable and low-latency communication (URLLC) are two key service types in the fifth-generation (5G) communication systems, pursuing scalability and reliability with low-latency, respectively. These two extreme services are envisaged to agglomerate together into \emph{critical mMTC} shortly with emerging use cases (e.g., wide-area disaster monitoring, wireless factory automation), creating new challenges to designing wireless systems beyond 5G. While conventional network slicing is effective in supporting a simple mixture of mMTC and URLLC, it is difficult to simultaneously guarantee the reliability, latency, and scalability requirements of critical mMTC (e.g., < 4ms latency, $10^6$ devices/km$^2$ for factory automation) with limited radio resources. Furthermore, recently proposed solutions to scalable URLLC (e.g., machine learning aided URLLC for driverless vehicles) are ill-suited to critical mMTC whose machine type users have minimal energy budget and computing capability that should be (tightly) optimized for given tasks. To this end, our paper aims to characterize promising use cases of critical mMTC and search for their possible solutions. To this end, we first review the state-of-the-art (SOTA) technologies for separate mMTC and URLLC services and then identify key challenges from conflicting SOTA requirements, followed by potential approaches to prospective critical mMTC solutions at different layers.