Multi‐omics studies promise the improved characterization of biological processes across molecular layers. However, methods for the unsupervised integration of the resulting heterogeneous data sets are lacking. We present Multi‐Omics Factor Analysis (MOFA), a computational method for discovering the principal sources of variation in multi‐omics data sets. MOFA infers a set of (hidden) factors that capture biological and technical sources of variability. It disentangles axes of heterogeneity that are shared across multiple modalities and those specific to individual data modalities. The learnt factors enable a variety of downstream analyses, including identification of sample subgroups, data imputation and the detection of outlier samples. We applied MOFA to a cohort of 200 patient samples of chronic lymphocytic leukaemia, profiled for somatic mutations, RNA expression, DNA methylation and ex vivo drug responses. MOFA identified major dimensions of disease heterogeneity, including immunoglobulin heavy‐chain variable region status, trisomy of chromosome 12 and previously underappreciated drivers, such as response to oxidative stress. In a second application, we used MOFA to analyse single‐cell multi‐omics data, identifying coordinated transcriptional and epigenetic changes along cell differentiation. Synopsis Multi‐Omics Factor Analysis (MOFA) is a computational framework for unsupervised discovery of the principal axes of biological and technical variation when multiple omics assays are applied to the same samples. MOFA is a broadly applicable approach for multi‐omics data integration. The inferred latent factors represent the underlying principal axes of heterogeneity across the samples. Factors can be shared by multiple data modalities or can be data‐type specific. The model flexibly handles missing values and different data types. In an application to Chronic Lymphocytic Leukaemia, MOFA discovers a low dimensional space spanned by known clinical markers and underappreciated axes of variation such as oxidative stress. In an application to multi‐omics profiles from single‐cells, MOFA recovers differentiation trajectories and identifies coordinated variation between the transcriptome and the epigenome. Multi‐Omics Factor Analysis (MOFA) is a computational framework for unsupervised discovery of the principal axes of biological and technical variation when multiple omics assays are applied to the same samples. MOFA is a broadly applicable approach for multi‐omics data integration.