This review describes the current state of magnetic criteria of aromaticity. The introduction contains the fundamentals of ring currents in aromatic and antiaromatic systems, followed by a brief description of experimental and computational tools: NMR, diamagnetic susceptibility exaltation, current density analyses (CDA) and nucleus independent chemical shifts (NICS). This is followed by more comprehensive chapters: NMR - focusing on the work of R. Mitchell - NICS and CDA - describing the progress and development of the methods to their current state and presenting some examples of representative work.