<p>Dimensionality reduction (DR) represents a fundamental preprocessing step in contemporary data analysis, particularly for datasets characterized by large feature spaces. While traditional linear techniques such as Principal Component Analysis (PCA) and Linear Discriminant Analysis (LDA) have long served as standard approaches in the field, they frequently encounter significant computational and scalability challenges when applied to extremely high-dimensional settings. In response to these limitations, random projection (RP) methods, particularly when integrated with complementary dimensionality reduction techniques or machine learning frameworks, have garnered increasing attention as viable alternatives, owing to their computational efficiency and robust theoretical guarantees for preserving essential data structures. This review systematically examines a range of hybrid DR approaches that leverage RP as a foundational component, elucidating their theoretical underpinnings, associated performance trade-offs, and practical deployment considerations across various application domains. Drawing on recent advances in the literature, we synthesize key insights and identify promising directions for future methodological development in this rapidly evolving field.</p>