Images captured through the glass often consist of undesirable specular reflections. These reflections detected in front of the glass remarkably reduce the quality and visibility of the scenes behind it. The process of reflection removal from images through the glass has many important applications in computer vision projects. Recently deep learning-based methods are being utilized for reflection removal so widely. In this article, we proposed a systematic literature review on the topic of single-image reflection removal using deep learning methods which were published between the years 2015 to 2021. A total number of 1600 research papers were extracted from five different online databases and digital libraries (IEEE Xplore, Google Scholar, Science Direct, SpringerLink and ACM Digital Library). After following the study selection procedure, 25 research papers were selected for this systematic review. The selected research papers were then analyzed to answer 7 key research questions that we have come up with to comprehensively explore the use of deep learning and neural networks for single-image reflection removal. After reading this article, future researchers will have a solid idea in the research field and will be able to work on their own research. The results provided in this proposed systematic review illustrate the main challenges that are encountered by researchers in this field and recommend encouraging directions for future research work. This review will also be helpful for researchers in discovering accessible datasets that can be used as benchmarks for comparing their proposed deep learning techniques with other studies in this research area.