As an important cornerstone of artificial intelligence, knowledge graph can extract and represent a priori knowledge from massive data on the Internet, which greatly solves the bottleneck problem of poorly interpretable cognitive decisions of intelligent systems and plays a key role in the construction and application of intelligent systems. As the application of knowledge graph technology continues to deepen, the work of knowledge graph completion, which aims to solve the problem of incompleteness of the graph, is imminent. Link prediction is the task of predicting the missing entities and relationships in the knowledge graph, which is an indispensable part of the construction and completion of the knowledge graph. To fully exploit the hidden relationships in the knowledge graph and to use the large number of entities and relationships for computation, it is necessary to convert the symbolic representation of information into numerical form, i.e., knowledge graph representation learning. Based on this, link prediction-oriented knowledge graph representation learning has become a hot research topic in the field of knowledge graphs. In this paper, we introduce the latest research progress of link prediction-oriented knowledge graph representation learning methods systematically from the basic concepts of link prediction and representation learning. In particular, the research progress is discussed in detail in terms of knowledge representation and algorithmic modeling. The development of the knowledge representation is used as a clue to introduce the mathematical modelling of link prediction tasks in the form of binary, multi-relational and hyper-relational knowledge representations respectively. Based on the representation learning modelling approach, the existing methods are refined into four types of models: translational distance models, tensor decomposition models, traditional deep learning models and graph neural network models, and the implementation of each type of model is described in detail together with representative models for solving link prediction tasks with different relational metrics. Based on the presentation of common datasets and criteria for link prediction, the results of four types of knowledge representation learning models for link prediction tasks with three types of knowledge representations are presented in a comparative analysis. Finally, the future development trends are presented in terms of model optimization, knowledge representation and problem scope.