  In this paper we discuss possible signatures for the production of scalar
\stst\ (stoponium) bound states \sigst\ at hadron colliders, where \st\ is the
lighter scalar top eigenstate. We first study the decay of \sigst; explicit
expressions are given for all potentially important decay modes. If \st\ has
unsuppressed two--body decays, they will always overwhelm the annihilation
decays of \sigst. Among the latter, we find that usually either the $gg$ or
$hh$ final state dominates, depending on the size of the off--diagonal entry of
the stop mass matrix; $h$ is the lighter neutral scalar Higgs boson of the
minimal supersymmetric model. If \msig\ happens to be close to the mass of one
of the neutral scalar Higgs bosons, $Q \bar{Q}$ final states dominate ($Q=b$ or
$t$). \ww\ and $ZZ$ final states are subdominant. We argue that $\sigst
\rightarrow \gamgam$ decays offer the best signal for stoponium production at
hadron colliders. The tevatron should be able to close the light stop window
left open by LEP searches, but its mass reach is limited to $\msig \leq 90$
GeV. In contrast, at the LHC one should ultimately be able to probe the region
$\msig \leq 700$ GeV, if the $hh$ partial width is not too large. We also
comment on the feasibility of searching for \sigst\ production at hadron
colliders in the $ZZ, \ Z \gamma$ and \fourtau\ final states, and briefly
mention \sigst\ production at \gamgam\ colliders.
