From the perspective of telecommunications, next-generation networks or beyond 5G will inevitably face the challenge of a growing number of users and devices. Such growth results in high-traffic generation with limited network resources. Thus, the analysis of the traffic and the precise forecast of user demands is essential for developing an intelligent network. In this line, Machine Learning (ML) and especially Deep Learning (DL) models can further benefit from the huge amount of network data. They can act in the background to analyze and predict traffic conditions more accurately than ever, and help to optimize the design and management of network services. Recently, a significant amount of research effort has been devoted to this area, greatly advancing network traffic prediction (NTP) abilities. In this paper, we bring together NTP and DL-based models and present recent advances in DL for NTP. We provide a detailed explanation of popular approaches and categorize the literature based on these approaches. Moreover, as a technical study, we conduct different data analyses and experiments with several DL-based models for traffic prediction. Finally, discussions regarding the challenges and future directions are provided.