Additive manufacturing (AM) has already proved itself to be the potential alternative to widely-used subtractive manufacturing due to its extraordinary capacity of manufacturing highly customized products with minimum material wastage. Nevertheless, it is still not being considered as the primary choice for the industry due to some of its major inherent challenges, including complex and dynamic process interactions, which are sometimes difficult to fully understand even with traditional machine learning because of the involvement of high-dimensional data such as images, point clouds, and voxels. However, the recent emergence of deep learning (DL) is showing great promise in overcoming many of these challenges as DL can automatically capture complex relationships from high-dimensional data without hand-crafted feature extraction. Therefore, the volume of research in the intersection of AM and DL is exponentially growing each year which makes it difficult for the researchers to keep track of the trend and future potential directions. Furthermore, to the best of our knowledge, there is no comprehensive review paper in this research track summarizing the recent studies. Therefore, this paper reviews the recent studies that apply DL for making the AM process better with a high-level summary of their contributions and limitations. Finally, it summarizes the current challenges and recommends some of the promising opportunities in this domain for further investigation with a special focus on generalizing DL models for wide-range of geometry types, managing uncertainties both in AM data and DL models, overcoming limited and noisy AM data issues by incorporating generative models, and unveiling the potential of interpretable DL for AM.