Due to the continuous digitalization of our society, distributed and web-based applications become omnipresent and making them more secure gains paramount relevance. Deep learning (DL) and its representation learning approach are increasingly been proposed for program code analysis potentially providing a powerful means in making software systems less vulnerable. This systematic literature review (SLR) is aiming for a thorough analysis and comparison of 32 primary studies on DL-based vulnerability analysis of program code. We found a rich variety of proposed analysis approaches, code embeddings and network topologies. We discuss these techniques and alternatives in detail. By compiling commonalities and differences in the approaches, we identify the current state of research in this area and discuss future directions. We also provide an overview of publicly available datasets in order to foster a stronger benchmarking of approaches. This SLR provides an overview and starting point for researchers interested in deep vulnerability analysis on program code.