Knowledge Graph Embedding (KGE) techniques play a pivotal role in transforming symbolic Knowledge Graphs (KGs) into numerical representations, thereby enhancing various deep learning models for knowledge-augmented applications. Unlike entities, relations in KGs are the carriers of semantic meaning, and their accurate modeling is crucial for the performance of KGE models. Firstly, we address the complex mapping properties inherent in relations, such as one-to-one, one-to-many, many-to-one, and many-to-many mappings. We provide a comprehensive summary of relation-aware mapping-based models, models that utilize specific representation spaces, tensor decomposition-based models, and neural network-based models. Next, focusing on capturing various relation patterns like symmetry, asymmetry, inversion, and composition, we review models that employ modified tensor decomposition, those based on modified relation-aware mappings, and those that leverage rotation operations. Subsequently, considering the implicit hierarchical relations among entities, we introduce models that incorporate auxiliary information, models based on hyperbolic spaces, and those that utilize the polar coordinate system. Finally, in response to more complex scenarios such as sparse and dynamic KGs, this paper discusses potential future research directions. We explore innovative ideas such as integrating multimodal information into KGE, enhancing relation pattern modeling with rules, and developing models to capture relation characteristics in dynamic KGE settings.