Conventionally, we think of Fermi surfaces as being the hallmark of normal metals, whereas superconductors have a gap towards quasiparticle excitations. In this talk, I will show that not only can superconductors have Fermi surfaces but these appear generically for a certain class of materials. The states at these Fermi surfaces do not describe bare electrons but Bogoliubov quasiparticles, i.e., superpositions of electrons and holes. The Bogoliubov Fermi surfaces appear for inversion-symmetric multiband superconductors that break time-reversal symmetry.

I will give an overview over the physics of this phenomenon, touching upon its physical explanation in terms of a pseudomagnetic field, associated topological invariants, and its instability against lattice deformations and towards other superconducting states. Moreover, I will contrast the phenomenon to Bogoliubov Fermi surfaces in materials without inversion symmetry, which have been proposed by G. Volovik, among others. Experimental signatures and candidate materials will also be discussed.