The development of advanced electrolyte materials for battery applications requires a detailed understanding of transport mechanisms. While electrochemical methods monitor overall charge transport, it is often relevant to clarify the role of the different electrolyte constituents in order to elucidate molecular mechanisms of transport. NMR spectroscopy methods are not only a valuable tool in chemical analytics, but NMR can be applied to monitor species-selective transport processes. For this purpose, magnetic field gradient pulses are applied to enable spatial resolution, with which diffusion coefficients can be determined in Pulsed Field Gradient (PFG)-NMR, also known as DOSY. A specialized application of PFG-NMR is the monitoring of molecular migration in an electric field: In electrophoretic NMR (eNMR) drift velocities and electrophoretic mobilities of molecular species are available, leading to a direct determination of the transference number T₊. This lecture describes applications to ionic migration in battery electrolytes, including ionic liquid- based electrolytes, concentrated liquid electrolytes and polymer electrolytes. By determination of the electrophoretic mobility of all molecular constituents, conclusions on speciation, i.e. the existence of transport-relevant ionic clusters, are drawn. Moreover, mobility data aid the quantification of ion-ion correlations (Onsager coefficients) in liquid electrolytes, which often pose a limitation to charge transport. In addition, for a large range of electrolytes, even including post-Li electrolytes based on Mg, K or Na, where electrochemical experiments become challenging, transference numbers T₊ can be provided to assess the electrolyte performance.