  Fast Radio Bursts (FRBs) are transient sources that emit a single radio pulse
with a duration of only a few milliseconds. Since the discovery of the first
FRB in 2007, tens of similar events have been detected. However, their physical
origin remains unclear, and a number of scenarios even larger than the number
of known FRBs has been proposed during these years. The presence of repeating
bursts in FRB 121102 allowed us to perform a precise localization of the source
with the Very Large Array and the European VLBI Network (EVN). Optical
observations with Keck, Gemini and HST unveiled the host to be a
low-metallicity star-forming dwarf galaxy located at a redshift of 0.193. The
EVN results showed that the bursts are co-located (within a projected
separation of $< 40$ pc) to a compact and persistent radio source with a size
of $< 0.7$ pc inside a star-forming region. This environment resembles the ones
where superluminous supernovae (SLSNe) or long gamma-ray bursts are produced.
Although the nature of this persistent source and the origin of the bursts
remain unknown, scenarios considering a pulsar/magnetar energizing a young
SLSN, or a system with a pulsar/magnetar in the vicinity of a massive black
hole are the most plausible ones to date. More recent observations have shown
that the bursts from FRB 121102 are almost 100% linearly polarized at an
unexpectedly high and variable Faraday rotation measure, that has been observed
to date only in vicinities of massive black holes. The bursts are thus likely
produced from a neutron star in such environment, although the system can still
be explained by a young neutron star embedded in a highly magnetized nebula.
Upcoming interferometric searches are expected to report tens of these
localizations in the coming years, unveil if this source is representative of
the whole population or a particular case, and dramatically boosting the field
of FRBs.
