Every data and kind of data need a physical drive to store it. There has been an explosion in the volume of images, video, and other similar data types circulated over the internet. Users using the internet expect intelligible data, even under the pressure of multiple resource constraints such as bandwidth bottleneck and noisy channels. Therefore, data compression is becoming a fundamental problem in wider engineering communities. There has been some related work on data compression using neural networks. Various machine learning approaches are currently applied in data compression techniques and tested to obtain better lossy and lossless compression results. A very efficient and variety of research is already available for image compression. However, this is not the case for video compression. Because of the explosion of big data and the excess use of cameras in various places globally, around 82% of the data generated involve videos. Proposed approaches have used Deep Neural Networks (DNNs), Recurrent Neural Networks (RNNs), and Generative Adversarial Networks (GANs), and various variants of Autoencoders (AEs) are used in their approaches. All newly proposed methods aim to increase performance (reducing bitrate up to 50% at the same data quality and complexity). This paper presents a bibliometric analysis and literature survey of all Deep Learning (DL) methods used in video compression in recent years. Scopus and Web of Science are well-known research databases. The results retrieved from them are used for this analytical study. Two types of analysis are performed on the extracted documents. They include quantitative and qualitative results. In quantitative analysis, records are analyzed based on their citations, keywords, source of publication, and country of publication. The qualitative analysis provides information on DL-based approaches for video compression, as well as the advantages, disadvantages, and challenges of using them.