The notion of a fast uplink grant is emerging as a promising solution for enabling massive machine type communications (MTCs) in the Internet of Things over cellular networks. By using the fast uplink grant, machine type devices (MTD) will no longer require random access (RA) channels to send scheduling requests. Instead, uplink resources can be actively allocated to MTDs by the base station. In this paper, the challenges and opportunities for adopting the fast uplink grant to support MTCs are investigated. First, the fundamentals of fast uplink grant and its advantages over conventional access schemes: i) fully scheduled with RA process and ii) uncoordinated access, are presented. Then, the key challenges that include the prediction of set of MTDs with data to transmit, as well as the optimal scheduling of MTDs, are exposed. To overcome these challenges, a two-stage approach that includes traffic prediction and optimized scheduling is proposed. For this approach, various solutions for source traffic prediction for periodic MTD traffic are reviewed and novel methods for event-driven traffic prediction are proposed. For optimal allocation of uplink grants, new solutions based on advanced machine learning methods are presented. By using the proposed solutions, the fast uplink grant has the potential to enable cellular networks to support massive MTCs and effectively reduce the signaling overhead and overcome the delay and congestion challenges of conventional RA schemes.