Cancer heterogeneity presents a major obstacle to effective drug treatment, emphasizing the need for personalized approaches that can accurately predict drug responses. Advances in high-throughput technologies have driven precision medicine initiatives toward integrating multi-omics data, enabling a more comprehensive understanding of tumor biology. However, integration of diverse omics layers poses challenges for computational modeling, as many traditional machine learning (ML) and statistical methods are not designed to capture complex, high-dimensional and multimodal data. This review examines the studies that integrate multi-omics datasets, aiming to enhance drug response prediction (DRP). Specifically, it outlines the most used omics types and computational approaches – classical ML models, as well as advanced deep learning and multimodal integration frameworks for improving DRP, detailing key methodologies and evaluation metrics, such as area under the dose–response curve, F1 score and mean square error, which assess model performance. By summarizing the integrated omics data, computational methods and challenges encountered, this review provides an in-depth overview of the existing landscape of precision medicine and future directions for advancing drug-response prediction.