The field of omics, driven by advances in high-throughput sequencing, faces a data explosion. This abundance of data offers unprecedented opportunities for predictive modeling in precision medicine, but also presents formidable challenges in data analysis and interpretation. Traditional machine learning (ML) techniques have been partly successful in generating predictive models for omics analysis but exhibit limitations in handling potential relationships within the data for more accurate prediction. This review explores a revolutionary shift in predictive modeling through the application of deep learning (DL), specifically convolutional neural networks (CNNs). Using transformation methods such as DeepInsight, omics data with independent variables in tabular (table-like, including vector) form can be turned into image-like representations, enabling CNNs to capture latent features effectively. This approach not only enhances predictive power but also leverages transfer learning, reducing computational time, and improving performance. However, integrating CNNs in predictive omics data analysis is not without challenges, including issues related to model interpretability, data heterogeneity, and data size. Addressing these challenges requires a multidisciplinary approach, involving collaborations between ML experts, bioinformatics researchers, biologists, and medical doctors. This review illuminates these complexities and charts a course for future research to unlock the full predictive potential of CNNs in omics data analysis and related fields.