The first part of the talk will focus on addressing the main technical challenges of quantitative myocardial perfusion MRI. This will cover the problem of respiratory motion in the images and the use of dimension reduction techniques, such as robust principal component analysis, to mitigate this problem. I will then discuss our deep learning-based image processing pipeline that solves the necessary series of computer vision tasks required for the blood flow modelling and introduce the Bayesian inference framework in which the kinetic parameter values are inferred from the imaging data. The second part of this talk will discuss some of the challenges of integrating deep learning models in clinical routine. This will cover recent work on building generalisable models that perform well when tested on unseen datasets acquired from distinct MRI scanners or clinical centres and work on learning in a data-efficient manner, without large training datasets, using synthesised data and physics-informed models.