Many software projects utilize Bug Tracking System (BTS) to manage and process bug reports. Over the years, the number of bug report submissions has increased exponentially with some projects receiving as many as about a hundred submissions daily. Bug report processing (BRP) consists of five key processes: duplicate detection, severity prediction, fix-time prediction, bug triage, and bug localization. Previously, traditional machine learning (ML) algorithms -based models were proposed to automate BRP tasks. However, in recent years deep BRP (DBRP) models were proposed to exploit the ever-increasing bug repositories for automatic extraction of semantic and contextual features of bug reports. Although, some papers reviewed related literature from many perspectives of software maintenance, no existing work comprehensively reviewed the state of DBRP. In this paper, we review the state of DBRP models in the five key BRP tasks. For this, we collect papers from four international databases published between 2015 and 2021. We evaluate the papers with regard to the deep neural networks, text representation models, and bug report features utilized. Finally, we present findings and prospects for future research works in DBRP. Our review analyzes how word embedding, CNNs, LSTMs, attention mechanism are used to represent bug report and source code, model performance and challenges such as data imbalance, feature utilization and complexity.