Despite the current success of myocardial tissue characterization with parametric mapping approaches, the accuracy and precision of T1, T2, T2* and ECV mapping can be affected by many confounding factors such as B0 and B1 inhomogeneity, respiratory and cardiac motion, heart rate variability, magnetisation transfer and other parameters. Moreover, estimation of T1, T2 and T2* is usually done by pixel-wise fitting of the MR signal to simple exponential models that may be an oversimplification of the true MR signal evolution. Here we will review the basic myocardial mapping techniques, discuss their pros and cons and subsequently discuss potential solutions.