  Accelerator searches for new resonances have a long-standing history of
discoveries that have driven advances in our understanding of nature. Since
2010, the Large Hadron Collider (LHC) has probed previously inaccessible energy
scales, allowing it to search for new heavy resonances predicted by a wide
range of theories beyond the standard model (BSM). In particular, resonance
decays into fermionic final states are often seen as golden channels since they
provide a clear signal, typically a peak in the invariant mass of the decay
products over a smoothly-falling background distribution. This review summaries
the key concepts of the experimental searches for new resonances decaying to
fermions, in the context of the BSM theories that motivate them, and presents
the latest results of the ATLAS and CMS experiments, focusing on the complete
LHC run-2 dataset. Future prospects at the high-luminosity LHC and potential
future colliders are also surveyed.
