  We review the theoretical and experimental situation for long-lived heavy
quarks, or bound states thereof, arising in simple extensions of the Standard
Model. If these particles propagate large distances before their decay, they
give rise to specific signatures requiring dedicated analysis methods. In
particular, vector-like quarks with negligible couplings to the three known
families could have eluded the past experimental searches. While most analyses
assume prompt decays at the production vertex, novel heavy quarks might lead to
signatures involving displaced vertices, new hadronic bound states, or decays
happening outside of the detector acceptance. We perform reinterpretations of
existing searches for short- and long-lived particles, and give suggestions on
how to extend their reach to long-lived heavy quarks.
