As an important cornerstone of artificial intelligence, knowledge graphs can extract and represent a priori knowledge from massive data on the Internet, which greatly solves the bottleneck problem of the poor interpretability of 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 knowledge graph completion that aims to solve the problem of the incompleteness of graphs is imminent. Link prediction is the task of predicting the missing entities and relations in the knowledge graph, which is indispensable in the construction and completion of the knowledge graph. The full exploitation of the hidden relations in the knowledge graph and the use of massive entities and relations for computation require the conversion of the symbolic representations of information into the numerical form, i.e., knowledge graph representation learning. Hence, link prediction-oriented knowledge graph representation learning has become a popular research topic in the field of knowledge graphs. This study systematically introduces the latest research progress of link prediction-oriented knowledge graph representation learning methods from the basic concepts of link prediction and representation learning. Specifically, the research progress is discussed in detail in terms of knowledge representation forms and algorithmic modeling methods. The development of the knowledge representation forms is used as a clue to introduce the mathematical modeling of link prediction tasks in the knowledge representation forms of binary relations, multi-relations, and hyper-relations. On the basis of the representation learning modeling, the existing methods are refined into four types of models: translation distance models, tensor decomposition models, traditional deep learning models, and graph neural network models. The implementation methods of each type are described in detail together with representative models for solving link prediction tasks with different relational metrics. The common datasets and criteria for link prediction are then introduced, and on this basis, the link prediction effects of the four types of knowledge representation learning models under the knowledge representation forms of binary relations, multi-relations, and hyper-relations are presented in a comparative analysis. Finally, the future development trends are given in terms of model optimization, knowledge representation forms, and problem scope.