High-Performance Computing (HPC) systems excel in managing distributed workloads, and the growing interest in Artificial Intelligence (AI) has resulted in a surge in demand for faster methods of Machine Learning (ML) model training and inference. In the past, research on HPC I/O focused on optimizing the underlying storage system for modeling and simulation applications and checkpointing the results, causing writes to be the dominant I/O operation. These applications typically access large portions of the data written by simulations or experiments. ML workloads, in contrast, perform small I/O reads spread across a large number of random files. This shift of I/O access patterns poses several challenges to HPC storage systems. In this paper, we survey I/O in ML applications on HPC systems, and target literature within a 6-year time window from 2019 to 2024. We provide an overview of the common phases of ML, review available profilers and benchmarks, examine the I/O patterns encountered during ML training, explore I/O optimizations utilized in modern ML frameworks and proposed in recent literature, and lastly, present gaps requiring further R&D. We seek to summarize the common practices used in accessing data by ML applications and expose research gaps that could spawn further R&D.