Deep learning (DL) has transformed applications in a variety of domains, including computer vision, natural language processing, and tabular data analysis. The search for improved DL model accuracy has led practitioners to explore increasingly large neural architectures, with some recent Transformer models spanning hundreds of billions of learnable parameters. These designs have introduced new scale-driven systems challenges for the DL space, such as memory bottlenecks, poor runtime efficiency, and high costs of model development. Efforts to address these issues have explored techniques such as parallelization of neural architectures, spilling data across the memory hierarchy, and memory-efficient data representations. This survey will explore the large-model training systems landscape, highlighting key challenges and the various techniques that have been used to address them.