Unconventional superconductivity in heavy-fermion compounds

•Quasiparticles in heavy-fermion compounds are much heavier than free electrons.•Superconductivity involves pairing of these massive quasiparticles.•Quasiparticle pairing mediated by magnetic or quadrupolar fluctuations.•We review the properties of superconductivity in heavy-fermion compounds.

Over the past 35 years, research on unconventional superconductivity in heavy-fermion systems has evolved from the surprising observations of unprecedented superconducting properties in compounds that convention dictated should not superconduct at all to performing explorations of rich phase spaces in which the delicate interplay between competing ground states appears to support emergent superconducting states. In this article, we review the current understanding of superconductivity in heavy-fermion compounds and identify a set of characteristics that is common to their unconventional superconducting states. These core properties are compared with those of other classes of unconventional superconductors such as the cuprates and iron-based superconductors. We conclude by speculating on the prospects for future research in this field and how new advances might contribute towards resolving the long-standing mystery of how unconventional superconductivity works.