With the development of modern high-throughput omic measurement platforms, it has become essential for biomedical studies to undertake an integrative (combined) approach to fully utilise these data to gain insights into biological systems. Data from various omics sources such as genetics, proteomics, and metabolomics can be integrated to unravel the intricate working of systems biology using machine learning-based predictive algorithms. Machine learning methods offer novel techniques to integrate and analyse the various omics data enabling the discovery of new biomarkers. These biomarkers have the potential to help in accurate disease prediction, patient stratification and delivery of precision medicine. This review paper explores different integrative machine learning methods which have been used to provide an in-depth understanding of biological systems during normal physiological functioning and in the presence of a disease. It provides insight and recommendations for interdisciplinary professionals who envisage employing machine learning skills in multi-omics studies.