Computational biology is essential in the process of translating biological knowledge into clinical practice, as well as in the understanding of biological phenomena based on the resources and technologies originating from the clinical environment. One such key contribution of computational biology is the discovery of biomarkers for predicting clinical outcomes using omic information. This process involves the predictive modelling and integration of different types of data and knowledge for screening, diagnostic or prognostic purposes. Moreover, this requires the design and combination of different methodologies based on statistical analysis and machine learning. This article introduces key computational approaches and applications to biomarker discovery based on different types of omic data. Although we emphasize applications in cardiovascular research, the computational requirements and advances discussed here are also relevant to other domains. We will start by introducing some of the contributions of computational biology to translational research, followed by an overview of methods and technologies used for the identification of biomarkers with predictive or classification value. The main types of omic approaches to biomarker discovery will be presented with specific examples from cardiovascular research. This will include a review of computational methodologies for single-source and integrative data applications. Major computational methods for model evaluation will be described together with recommendations for reporting models and results. We will present recent advances in cardiovascular biomarker discovery based on the combination of gene expression and functional network analyses. The review will conclude with a discussion of key challenges for computational biology, including perspectives from the biosciences and clinical areas.