Direct-photon pair production in high-energy hadron collisions is considered. After discussing general aspects of such reactions and giving a brief historical survey of the subject, we present some calculations on the contributions from $q\overline{q}$ and $\mathrm{gg}$ collisions (the latter via the quark box) to the $\ensuremath{\gamma}\ensuremath{\gamma}$ continuum, and on possible resonant contributions. Finally, an estimation of the indirect-photon background (mainly due to ${\ensuremath{\pi}}^{0}$ and $\ensuremath{\eta}$ decay, and to quark bremsstrahlung) is given for colliding-beam conditions at high energy; assuming both photons to be measured at 90\ifmmode^\circ\else\textdegree\fi{} with equal and opposite momenta, and (within experimental limits) unaccompanied by any hadrons or additional photons, it is shown that this background can be sharply reduced.