Quantum mechanical band-to-band tunneling is a type of carrier injection mechanism that is responsible for the electronic transport in devices like tunnel field effect transistors (TFETs), which hold great promise in reducing the subthreshold swing below the Boltzmann limit. This allows scaling down the operating voltage and the off-state leakage current at the same time, and thus reducing the power consumption of metal oxide semiconductor transistors. Conventional group IV or compound semiconductor materials suffer from interface and bulk traps, which hinder the device performance because of the increased trap-induced parasitics. Alternatives like two-dimensional materials (2DMs) are beneficial for realizing such devices due to their ultra-thin body and atomically sharp interfaces with van der Waals interactions, which significantly reduce the trap density, compared to their bulk counterparts, and hold the promise to finally achieve the desired low-voltage operation. In this review, we summarize the recent progress on such devices, with a major focus on heterojunctions made of different 2DMs. We review different types of emerging device concepts, architectures, and the tunneling mechanisms involved by analytically studying various simulations and experimental devices. We present our detailed perspective on the current developments, major roadblocks, and key strategies for further improvements of the TFET technology based on 2D heterojunctions to match industry requirements. The main goal of this paper is to introduce the reader to the concept of tunneling especially in van der Waals devices and provide an overview of the recent progress and challenges in the field.