For many complex diseases, an earlier and more reliable diagnosis is considered a key prerequisite for developing more effective therapies to prevent or delay disease progression. Classical statistical learning approaches for specimen classification using omics data, however, often cannot provide diagnostic models with sufficient accuracy and robustness for heterogeneous diseases like cancers or neurodegenerative disorders. In recent years, new approaches for building multivariate biomarker models on omics data have been proposed, which exploit prior biological knowledge from molecular networks and cellular pathways to address these limitations. This survey provides an overview of these recent developments and compares pathway- and network-based specimen classification approaches in terms of their utility for improving model robustness, accuracy and biological interpretability. Different routes to translate omics-based multifactorial biomarker models into clinical diagnostic tests are discussed, and a previous study is presented as example.