The recording of the electrocardiogram (ECG) during magnetic resonance imaging (MRI) acquisition is of great interest and importance. Firstly, MRI acquisition is a relatively slow process, which therefore complicates the imaging of moving organs. Cardiac MRI requires the development of strategies for acquiring high quality images, which is mainly achieved by synchronising the image acquisition with a specific time during the cardiac cycle. The ECG is used to monitor the heart's activity, and the detection of the largest and steepest peak in the cardiac cycle (the QRS complex) triggers the acquisition of slices of the k-space. Secondly, patients undergoing an MRI examination need to be monitored for safety during the procedure, and therefore ECG signals are used to track their cardiovascular state in real time. However, there are significant barriers to the accurate observation and processing of the ECG during MRI acquisition. In particular, the flow of charged blood particles through the large applied magnetic field leads to an extra current source, known as the magnetohdrodymanic (MHD) effect. This review article discusses these barriers and state-of-the-art solutions. An overview of the relevant technology including hardware and applications are described. The development of new software tools for the processing of the ECG signals acquired during MRI is also detailed. These developments include the design of specific QRS detection algorithms, which are able to distinguish QRS complexes from the MHD effect but also the gradient artefacts. Different techniques for the suppression of the gradient artefacts are also presented as well as the most challenging problem to-date-the problem of separating the MHD effect from the ECG. The article concludes by summarising the advantages of using ECG signals during MRI, but also presents the current limitations of modern analysis techniques in this domain. The most promising avenues of research are also discussed and suggestions for new methodological analyses for the development of this field are given.