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 a subpercent level for primordial black holes as light as O(0.01) M_{⊙} 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.
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