Rapid innovations in cardiovascular magnetic resonance (CMR) now permit the routine acquisition of quantitative measures of myocardial and blood T1 which are key tissue characteristics. These capabilities introduce a new frontier in cardiology, enabling the practitioner/investigator to quantify biologically important myocardial properties that otherwise can be difficult to ascertain clinically. CMR may be able to track biologically important changes in the myocardium by: a) native T1 that reflects myocardial disease involving the myocyte and interstitium without use of gadolinium based contrast agents (GBCA), or b) the extracellular volume fraction (ECV)-a direct GBCA-based measurement of the size of the extracellular space, reflecting interstitial disease. The latter technique attempts to dichotomize the myocardium into its cellular and interstitial components with estimates expressed as volume fractions. This document provides recommendations for clinical and research T1 and ECV measurement, based on published evidence when available and expert consensus when not. We address site preparation, scan type, scan planning and acquisition, quality control, visualisation and analysis, technical development. We also address controversies in the field. While ECV and native T1 mapping appear destined to affect clinical decision making, they lack multi-centre application and face significant challenges, which demand a community-wide approach among stakeholders. At present, ECV and native T1 mapping appear sufficiently robust for many diseases; yet more research is required before a large-scale application for clinical decision-making can be recommended.