Predictive monitoring of business processes is concerned with the prediction of ongoing cases on a business process. Lately, the popularity of deep learning techniques has propitiated an ever-growing set of approaches focused on predictive monitoring based on these techniques. However, the high disparity of process logs and experimental setups used to evaluate these approaches makes it especially difficult to make a fair comparison. Furthermore, it also difficults the selection of the most suitable approach to solve a specific problem. In this paper, we provide both a systematic literature review of approaches that use deep learning to tackle the predictive monitoring tasks. In addition, we performed an exhaustive experimental evaluation of 10 different approaches over 12 publicly available process logs.