Entity embeddings have gained significant attention in machine learning and natural language processing for representing discrete categorical variables or entities as dense, low-dimensional continuous vectors that capture semantic and relational information. Foundational research demonstrates their effectiveness in improving model performance for tasks such as recommendation systems, knowledge graph representation, categorical feature modeling, and structured prediction. Recent studies extend entity embeddings to graph neural networks, relational learning, and multimodal applications, enabling models to capture complex dependencies among entities and integrate heterogeneous data sources. Methods leveraging supervised, unsupervised, and self-supervised learning approaches—including translational models (e.g., TransE, TransH), graph embeddings (e.g., node2vec, GraphSAGE), and attention-based architectures—have been applied to entity resolution, link prediction, semantic search, and question answering. The research also explores transfer learning and domain adaptation for entity embeddings to improve generalization across tasks and datasets, establishing them as a foundational tool for embedding discrete data in deep learning pipelines.