The online social platforms, like Twitter, Facebook, LinkedIn and WeChat, have grown really fast in last decade and have been one of the most effective platforms for people to communicate and share information with each other. Due to the "word of mouth" effects, information usually can spread rapidly on these social media platforms. Therefore, it is important to study the mechanisms driving the information diffusion and quantify the consequence of information spread. A lot of efforts have been focused on this problem to help us better understand and achieve higher performance in viral marketing and advertising. On the other hand, the development of neural networks has blossomed in the last few years, leading to a large number of graph representation learning (GRL) models. Compared to traditional models, GRL methods are often shown to be more effective. In this paper, we present a comprehensive review for existing works using GRL methods for popularity prediction problem, and categorize related literatures into two big classes, according to their mainly used model and techniques: embedding-based methods and deep learning methods. Deep learning method is further classified into six small classes: convolutional neural networks, graph convolutional networks, graph attention networks, graph neural networks, recurrent neural networks, and reinforcement learning. We compare the performance of these different models and discuss their strengths and limitations. Finally, we outline the challenges and future chances for popularity prediction problem.