Qualitative MRI methods, such as T2-weighted (T2W) imaging, are used to study cardiac tissue in numerous pathologies, but these methods are sensitive to artefacts, and results can be unreliable. Modified Look-Locker inversion recovery (MOLLI) provides robust, quantitative T1 estimates in the myocardium, but limitations include: dependence on heart rate; banding artefacts; and lengthy breath-holds. In this work, I developed new MOLLI variants to mitigate these problems and applied MOLLI to two different patient groups for comparison with conventional methods. The MOLLI variants used alternative k-space trajectories, readouts, startup preparations, and sampling schemes, and were tested in silico and in vitro, and in vivo in healthy volunteers. In patients, MOLLI was compared to T2W-SPAIR for oedema detection in acute ST-segment elevation myocardial infarction (STEMI) and takotsubo cardiomyopathy (TCM). Development work showed that a linear sweep up (skipped pulse pair) startup preparation improved T1 measurements, while a truncated MOLLI scheme performed similarly to conventional MOLLI, permitting shorter breath holds. Different k-space trajectories did not significantly affect T1 measurement accuracy, but precision varied: possibly due to artefacts. In patients, MOLLI performed significantly better than T2W-SPAIR in STEMI, while the two were comparable in TCM. In all patients, remote myocardium showed an elevated T1 versus healthy volunteers, suggesting remote inflammation. In conclusion, MOLLI T1 mapping can delineate oedema in acute STEMI and TCM, producing measurements more robust and reproducible than those made with T2W SPAIR. Several improvements were suggested here, but there is still substantial scope for developing MOLLI T1 mapping in future.