  The top quark plays a central role in particle physics, as many experiments
at the Large Hadron Collider scrutinize its properties within the Standard
Model. Although most of the measurements of the top quarks today concentrate on
production modes initiated by quarks or gluons, this review will highlight the
lesser-explored modes initiated by pomerons or photons. It aims to provide an
in-depth look into both the phenomenological studies and the existing
experimental measurements, emphasizing the necessity of exploring the
diffractive and photon-induced production of top quarks to enhance the accuracy
of top-quark measurements.
