With the advancement in technology and the expansion of broadcasting, cross-media retrieval has gained much attention. It plays a significant role in big data applications and consists in searching and finding data from different types of media. In this paper, we provide a novel taxonomy according to the challenges faced by multi-modal deep learning approaches in solving cross-media retrieval, namely: representation, alignment, and translation. These challenges are evaluated on deep learning (DL) based methods, which are categorized into four main groups: 1) unsupervised methods, 2) supervised methods, 3) pairwise based methods, and 4) rank based methods. Then, we present some well-known cross-media datasets used for retrieval, considering the importance of these datasets in the context in of deep learning based cross-media retrieval approaches. Moreover, we also present an extensive review of the state-of-the-art problems and its corresponding solutions for encouraging deep learning in cross-media retrieval. The fundamental objective of this work is to exploit Deep Neural Networks (DNNs) for bridging the "media gap", and provide researchers and developers with a better understanding of the underlying problems and the potential solutions of deep learning assisted cross-media retrieval. To the best of our knowledge, this is the first comprehensive survey to address cross-media retrieval under deep learning methods.