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Deep multi-modal learning, a rapidly growing field with a wide range of practical applica‐ tions, aims to effectively utilize and integrate information from multiple sources, known as modalities. Despite its impressive empirical performance, the theoretical foundations of deep multi-modal learning have yet to be fully explored. In this paper, we will undertake a comprehensive survey of recent devel‐ opments in multi-modal learning theories, focusing on the fundamental properties that govern this field. Our goal is to provide a thorough collection of current theoretical tools for analyzing multi-modal learn‐ ing, to clarify their implications for practitioners, and to suggest future directions for the establishment of a solid theoretical foundation for deep multi-modal learning. [ABSTRACT FROM AUTHOR]