Recent developments in Generative AI, Computer Vision, and Natural Language Processing have led to an increased integration of AI models into various products. This widespread adoption of AI requires significant efforts in deploying these models in production environments. When hosting machine learning models for real-time predictions, it is important to meet defined Service Level Objectives (SLOs), ensuring reliability, minimal downtime, and optimizing operational costs of the underlying infrastructure. Large machine learning models often demand GPU resources for efficient inference to meet SLOs. In the context of these trends, there is growing interest in hosting AI models in a serverless architecture while still providing GPU access for inference tasks. This survey aims to summarize and categorize the emerging challenges and optimization opportunities for large-scale deep learning serving systems. By providing a novel taxonomy and summarizing recent trends, we hope that this survey could shed light on new optimization perspectives and motivate novel works in large-scale deep learning serving systems.