Massive multiple-input multiple-output (MIMO) systems are a main enabler of the excessive throughput requirements in 5G and future generation wireless networks as they can serve many users simultaneously with high spectral and energy efficiency. To achieve this, massive MIMO systems require accurate and timely channel state information (CSI), which is acquired by a training process that involves pilot transmission, CSI estimation and feedback. This training process incurs a training overhead, which scales with the number of antennas, users and subcarriers. Reducing this training overhead in massive MIMO systems has been a major topic of research since the emergence of the concept. Recently, deep learning (DL)-based approaches for massive MIMO training have been proposed and showed significant improvements compared to traditional techniques. This paper provides an overview of how neural networks (NNs) can be used in the training process of massive MIMO systems to improve the performance by reducing the CSI acquisition overhead and to reduce complexity.