  Primordial black holes possibly formed in the early universe could provide a
significant fraction of the dark matter and would be unique probes of
inflation. A smoking gun for their discovery would be the detection of a
subsolar mass compact object. We argue that extreme mass-ratio inspirals will
be ideal to search for subsolar-mass black holes not only with LISA but also
with third-generation ground-based detectors such as Cosmic Explorer and the
Einstein Telescope. These sources can provide unparalleled measurements of the
mass of the secondary object at subpercent level for primordial black holes as
light as ${\cal O}(0.01)M_\odot$ up to luminosity distances around hundred
megaparsec and few gigaparsec for LISA and Einstein Telescope, respectively, in
a complementary frequency range. This would allow claiming, with very high
statistical confidence, the detection of a subsolar-mass black hole, which
would also provide a novel (and currently undetectable) family of sources for
third-generation detectors.
