Fast Radio Bursts (FRBs) are fast, millisecond-duration, extremely bright (~Jy) bursts that have so far only been observed at radio wavelengths. Only a small fraction of them, the so called repeaters, have been observed more than once and their multiple detections have shaped the theories on their -still nebulous- origin towards a possible young magnetar progenitor. The recent localisation of the very active, nearby (150 Mpc) repeater, FRB 180916, for which, for the first time, periodicity was also identified (a 5 day active cycle every 16.3 days) sparked new life into the search of multiwavelength counterparts. In addition to this, the last year has witnessed the first possible smoking gun of a magnetar-FRB connection with the detection of X-ray emission accompanying the radio burst. I will present an overview of the efforts towards the detection of the -so far elusive- multiwavelength counterpart of an FRB, with particular emphasis on the work led by Italian teams in radio, optical, X-rays and gamma-rays. I will discuss the challenges to this task in light of models' predictions and will outline the future prospects for multiwavelength campaigns targeting repeater FRBs.