  Leptoquarks can be produced in pairs by gluon--gluon fusion and
quark--antiquark annihilation at hadron colliders. While HERA is the proper
machine for single production of $(eu)$ and $(ed)$ type leptoquarks, the flavor
species of ($\mu u$), ($\mu d$) and ($\tau u$), ($\tau d$) type leptoquarks can
be produced at hadron colliders very efficiently. Besides exploiting
gluon-quark collisions, leptoquarks can also be produced singly by colliding
the quarks in one proton beam with leptons $e,\mu,\tau$ generated by splitting
photons which are radiated off the quarks in the other proton beam. For Yukawa
couplings of the size $\alpha$ leptoquark masses up to about 300~GeV can be
generated at the Tevatron while the LHC can produce leptoquarks with masses up
to about 3~TeV. [Leptoquarks involving heavy quarks can be produced singly at a
lower rate, determined by the heavy flavor flux in the proton beam.]
