The central challenge in massive machine-type communications (mMTC) is to connect a large number of uncoordinated devices through a limited spectrum. The typical mMTC communication pattern is sporadic, with short packets. This could be exploited in grant-free random access in which the activity detection, channel estimation, and data recovery are formulated as a sparse recovery problem and solved via compressed sensing algorithms. This approach results in new challenges in terms of high computational complexity and latency. We present how data-driven methods can be applied in grant-free random access and demonstrate the performance gains. Variations of neural networks for the problem are discussed, as well as future challenges and potential directions.