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Artificial Intelligence techniques powered by deep neural nets have achieved much success in several application domains, most significantly and notably in the Computer Vision applications and Natural Language Processing tasks. Surpassing human-level performance propelled the research in the applications where different modalities amongst language, vision, sensory, text play an important role in accurate predictions and identification. Several multimodal fusion methods employing deep learning models are proposed in the literature. Despite their outstanding performance, the complex, opaque and black-box nature of the deep neural nets limits their social acceptance and usability. This has given rise to the quest for model interpretability and explainability, more so in the complex tasks involving multimodal AI methods. This paper extensively reviews the present literature to present a comprehensive survey and commentary on the explainability in multimodal deep neural nets, especially for the vision and language tasks. Several topics on multimodal AI and its applications for generic domains have been covered in this paper, including the significance, datasets, fundamental building blocks of the methods and techniques, challenges, applications, and future trends in this domain