Deep Neural Networks (DNNs) trained on one dataset (source domain) do not perform well on another set of data (target domain), which is different but has similar properties as the source domain. Domain Adaptation (DA) strives to alleviate this problem and has great potential in its application in practical settings, real-world scenarios, industrial applications and many data domains. Various DA methods aimed at individual data domains have been reported in the last few years; however, there is no comprehensive survey that encompasses all these data domains, focuses on the datasets available, the methods relevant to each domain, and importantly the applications and challenges. To that end, this survey paper discusses how DA can help DNNs work efficiently in these settings by reviewing DA methods and techniques. We have considered five data domains: computer vision, natural language processing, speech, time-series, and multi-modal data. We present a comprehensive taxonomy, including the methods, datasets, challenges, and applications corresponding to each domain. Our goal is to discuss industrial use cases and DA implementation for those. Our final aim is to provide future research directions based on evolving methods and results, the datasets used, and industrial applications.