Realizing the potential gains of large-scale MIMO systems requires the accurate estimation of their channels or the fine adjustment of their narrow beams. This, however, is typically associated with high channel acquisition/beam sweeping overhead that scales with the number of antennas. Machine and deep learning represent promising approaches to overcome these challenges thanks to their powerful ability to learn from prior observations and side information. Training machine and deep learning models, however, requires large-scale datasets that are expensive to collect in deployed systems. To address this challenge, we propose a novel direction that utilizes digital replicas of the physical world to reduce or even eliminate the MIMO channel acquisition overhead. In the proposed digital twin aided communication, 3D models that approximate the real-world communication environment are constructed and accurate ray-tracing is utilized to simulate the site-specific channels. These channels can then be used to aid various communication tasks. Further, we propose to use machine learning to approximate the digital replicas and reduce the ray tracing computational cost. To evaluate the proposed digital twin based approach, we conduct a case study focusing on the position-aided beam prediction task. The results show that a learning model trained solely with the data generated by the digital replica can achieve relatively good performance on the real-world data. Moreover, a small number of real-world data points can quickly achieve near-optimal performance, overcoming the modeling mismatches between the physical and digital worlds and significantly reducing the data acquisition overhead.