Parametric mapping of the heart has become an essential part of many cardiovascular magnetic resonance imaging exams, and is used for tissue characterization and diagnosis in a broad range of cardiovascular diseases. These pulse sequences are used to quantify the myocardial T ₁ , T ₂ , , and T _1ρ relaxation times, which are unique surrogate indices of fibrosis, edema and iron deposition that can be used to monitor a disease over time or to compare patients to one another. Parametric mapping is now well-accepted in the clinical setting, but its wider dissemination is hindered by limited inter-center reproducibility and relatively long acquisition times. Recently, several new parametric mapping techniques have appeared that address both of these problems, but substantial hurdles remain for widespread clinical adoption. This review serves both as a primer for newcomers to the field of parametric mapping and as a technical update for those already well at home in it. It aims to establish what is currently needed to improve the reproducibility of parametric mapping of the heart. To this end, we first give an overview of the metrics by which a mapping technique can be assessed, such as bias and variability, as well as the basic physics behind the relaxation times themselves and what their relevance is in the prospect of myocardial tissue characterization. This is followed by a summary of routine mapping techniques and their variations. The problems in reproducibility and the sources of bias and variability of these techniques are reviewed. Subsequently, novel fast, whole-heart, and multi-parametric techniques and their merits are treated in the light of their reproducibility. This includes state of the art segmentation techniques applied to parametric maps, and how artificial intelligence is being harnessed to solve this long-standing conundrum. We finish up by sketching an outlook on the road toward inter-center reproducibility, and what to expect in the future.