  The origin and phenomenology of the Fast Radio Burst (FRB) remains unknown
despite more than a decade of efforts. Though several models have been proposed
to explain the observed data, none is able to explain alone the variety of
events so far recorded. The leading models consider magnetars as potential FRB
sources. The recent detection of FRBs from the galactic magnetar SGR J1935+2154
seems to support them. Still, emission duration and energetic budget challenge
all these models. Like for other classes of objects initially detected in a
single band, it appeared clear that any solution to the FRB enigma could only
come from a coordinated observational and theoretical effort in an as wide as
possible energy band. In particular, the detection and localisation of
optical/NIR or/and high-energy counterparts seemed an unavoidable starting
point that could shed light on the FRB physics. Multiwavelength (MWL) search
campaigns were conducted for several FRBs, in particular for repeaters. Here we
summarize the observational and theoretical results and the perspectives in
view of the several new sources accurately localised that will likely be
identified by various radio facilities worldwide. We conclude that more
dedicated MWL campaigns sensitive to the millisecond--minute timescale
transients are needed to address the various aspects involved in the
identification of FRB counterparts. Dedicated instrumentation could be one of
the key points in this respect. In the optical/NIR band, fast photometry looks
to be the only viable strategy. Additionally, small/medium size radiotelescopes
co-pointing higher energies telescopes look a very interesting and cheap
complementary observational strategy.
