The rapid improvement of next-generation sequencing (NGS) technologies and their application in large-scale cohorts in cancer research led to common challenges of big data. It opened a new research area incorporating systems biology and machine learning. As large-scale NGS data accumulated, sophisticated data analysis methods became indispensable. In addition, NGS data have been integrated with systems biology to build better predictive models to determine the characteristics of tumors and tumor subtypes. Therefore, various machine learning algorithms were introduced to identify underlying biological mechanisms. In this work, we review novel technologies developed for NGS data analysis, and we describe how these computational methodologies integrate systems biology and omics data. Subsequently, we discuss how deep neural networks outperform other approaches, the potential of graph neural networks (GNN) in systems biology, and the limitations in NGS biomedical research. To reflect on the various challenges and corresponding computational solutions, we will discuss the following three topics: (i) molecular characteristics, (ii) tumor heterogeneity, and (iii) drug discovery. We conclude that machine learning and network-based approaches can add valuable insights and build highly accurate models. However, a well-informed choice of learning algorithm and biological network information is crucial for the success of each specific research question.