Recent developments in high-throughput DNA sequencing technology allowed the generation of data at multiple omics levels, including genomics, transcriptomics, proteomics, metabolomics and radiomics. All these structured data offer enormous potential for understanding disease mechanisms, but their high dimensionality, noise, redundancy and heterogeneity pose various challenges to their analysis. Traditional methods often struggle to effectively integrate and extract meaningful patterns from such data. The aim of this paper is twofold: (i) to briefly review the models and methods proposed in the literature for multi-omics data integration, focusing on unsupervised learning approaches, and particularly non-negative matrix factorizations; (ii) to present a novel joint non-negative matrix tri-factorization (NMTF) model for multi-omics data analysis, which is proposed to better address some of the challenges associated with multi-omics data analysis, capturing complex gene expression patterns while maintaining biological interpretability through its non-negativity constraints.