Most biological mechanisms involve more than one type of biomolecule, and hence operate not solely at the level of either genome, transcriptome, proteome, metabolome or ionome. Datasets resulting from single-omic analysis are rapidly increasing in throughput and quality, rendering multi-omic studies feasible. These should offer a comprehensive, structured and interactive overview of a biological mechanism. However, combining single-omic datasets in a meaningful manner has so far proved challenging, and the discovery of new biological information lags behind expectation. One reason is that experiments conducted in different laboratories can typically not to be combined without restriction. Second, the interpretation of multi-omic datasets represents a significant challenge by nature, as the biological datasets are heterogeneous not only for technical, but also for biological, chemical, and physical reasons. Here, multi-layer network theory and methods of artificial intelligence might contribute to solve these problems. For the efficient application of machine learning however, biological datasets need to become more systematic, more precise - and much larger. We conclude our review with basic guidelines for the successful set-up of a multi-omic experiment.