Quantum computers have the potential to provide an advantage over classical computers in a number of areas. Numerous metrics to benchmark the performance of quantum computers, ranging from their individual hardware components to entire applications, have been proposed over the years. Navigating the resulting extensive literature can be overwhelming. Objective comparisons are further hampered in practice as different variations of the same metric are used, and the data disclosed together with a reported metric value is often not sufficient to reproduce the measurements. This article addresses these challenges by providing a review of metrics and benchmarks for quantum computers and 1) a comprehensive collection of benchmarks allowing holistic comparisons of quantum computers, 2) a consistent format of the definitions across all metrics including a transparent description of the methodology and of the main assumptions and limitations, and 3) a reproducible approach by linking the metrics to open-source software used to evaluate them.We identify five areas where international standardization working groups could be established, namely: i) the identification and agreement on the categories of metrics that comprehensively benchmark device performance; ii) the identification and agreement on a set of well-established metrics that together comprehensively benchmark performance; iii) the identification of metrics specific to hardware platforms, including non-gate-based quantum computers; iv) inter-laboratory comparison studies to develop best practice guides for measurement methodology; and v) agreement on what data and software should be reported together with a metric value to ensure trust, transparency and reproducibility. We provide potential routes to advancing these areas. We expect this compendium to accelerate the progress of quantum computing hardware towards quantum advantage.