In this work, system monitoring and analysis are discussed in terms of their significance and benefits for operations and research in the field of high-performance computing (HPC). HPC systems deliver unique insights to computational scientists from different disciplines. It is argued that research in HPC is also computational in nature, given the massive amounts of monitoring data collected at various levels of an HPC system. The vision of a comprehensive system model developed based on holistic monitoring and analysis is also presented. The goal and expected outcome of such a model is an improved understanding of the intricate interactions between today's software and hardware, and their diverse usage patterns. The associated modeling, monitoring, and analysis challenges are reviewed and discussed. The envisioned comprehensive system model will provide the ability to design future systems that are better understood before use, easier to maintain and monitor, more efficient, more reliable, and, therefore, more productive. The paper is concluded with a number of recommendations towards realizing the envisioned system model.