The innovation of biotechnologies has allowed the accumulation of omics data at an alarming rate, thus introducing the era of 'big data'. Extracting inherent valuable knowledge from various omics data remains a daunting problem in bioinformatics. Better solutions often need some kind of more innovative methods for efficient handlings and effective results. Recent advancements in integrated analysis and computational modeling of multi-omics data helped address such needs in an increasingly harmonious manner. The development and application of machine learning have largely advanced our insights into biology and biomedicine and greatly promoted the development of therapeutic strategies, especially for precision medicine. Here, we propose a comprehensive survey and discussion on what happened, is happening and will happen when machine learning meets omics. Specifically, we describe how artificial intelligence can be applied to omics studies and review recent advancements at the interface between machine learning and the ever-widest range of omics including genomics, transcriptomics, proteomics, metabolomics, radiomics, as well as those at the single-cell resolution. We also discuss and provide a synthesis of ideas, new insights, current challenges and perspectives of machine learning in omics.