  Vector-like quarks are featured by a wealth of beyond the Standard Model
theories and are consequently an important goal of many LHC searches for new
physics. Those searches, as well as most related phenomenological studies,
however rely on predictions evaluated at the leading-order accuracy in QCD and
consider well-defined simplified benchmark scenarios. Adopting an effective
bottom-up approach, we compute next-to-leading-order predictions for
vector-like-quark pair-production and single production in association with
jets, with a weak or with a Higgs boson in a general new physics setup. We
additionally compute vector-like-quark contributions to the production of a
pair of Standard Model bosons at the same level of accuracy. For all processes
under consideration, we focus both on total cross sections and on differential
distributions, most these calculations being performed for the first time in
our field. As a result, our work paves the way to precise extraction of
experimental limits on vector-like quarks thanks to an accurate control of the
shapes of the relevant observables and emphasize the extra handles that could
be provided by novel vector-like-quark probes never envisaged so far
