Understanding ancient organisms and their paleo-environments through the study of body fossils represents a central tenet of paleontology. Advances in digital image capture over the past several decades now allow for efficient and accurate documentation, curation and interrogation of fossil anatomy over disparate length scales. Despite these developments, key body fossil image processing and analysis tasks, such as segmentation and classification still require significant user intervention, which can be labor-intensive and subject to human bias. Recent advancements in deep learning offer the potential to automate fossil image analysis while improving throughput and limiting operator bias. Despite the recent emergence of deep learning within paleontology, challenges such as the scarcity of diverse, high quality image datasets and the complexity of fossil morphology necessitate further advancements and the adoption of concepts from other scientific domains. Here, we comprehensively review state-of-the-art deep learning-based methodologies applied towards body fossil analysis while grouping the studies based on the fossil type and nature of the task. Furthermore, we analyze existing literature to tabulate dataset information, neural network architecture type, key results, and comprehensive textual summaries. Finally, based on the collective limitations of the existing studies, we discuss novel techniques for fossil data augmentation and fossil image enhancements, which can be combined with advanced neural network architectures, such as diffusion models, generative hybrid networks, transformers, and graph neural networks, to improve body fossil image analysis.