  We review the theory and phenomenology of isosinglet vector-like quarks
(VLQs). In recent years, interest in VLQs has been increasing, due to their
contributions to new physics effects that can be tested in experiments at LHC
and High-Luminosity LHC. The similarities of models with isosinglet VLQs and
the seesaw framework in the leptonic sector are pointed out. The existence of
VLQs leads to flavour-changing neutral currents at tree level and deviations
from unitarity of the CKM matrix, introducing rich phenomenological
implications. These new effects are naturally suppressed by the masses of the
new quarks, that are constrained to be above the electroweak scale. In
addition, striking new effects can be achieved with the inclusion of an extra
complex scalar singlet. Such a minimal extension of the SM can give rise to new
sources of CP violation with profound theoretical implications, allowing for a
solution to the strong CP problem and a possible explanation for the baryon
asymmetry of the Universe. We list and explain strong motivations to consider
this class of models. We also briefly review how models with VLQs can be
matched to the SM effective field theory (SMEFT). A detailed analysis of
flavour observables that can be affected by the presence of VLQs is presented.
Current bounds from collider searches of VLQs are summarized. We point out that
the discovery of VLQs can be within the reach of present or future colliders
being planned.
