  We perform lattice calculations of the lightest J=0,2,4,6 glueball masses in
the D=3+1 SU(3) gauge theory and extrapolate to the continuum limit. Assuming
that these masses lie on linear Regge trajectories we find a leading glueball
trajectory alpha(t)=0.93(24) + 0.28(2)alpha'_R t, where alpha'_R ~ 0.9 GeV^{-2}
is the slope of the usual mesonic Regge trajectory. This glueball trajectory
has an intercept and slope similar to that of the Pomeron trajectory. We
contrast this with the situation in D=2+1 where the leading glueball Regge
trajectory is found to have too small an intercept to be important for
high-energy cross-sections. We interpret the observed states and trajectories
in terms of open and closed string models of glueballs. We discuss the large-N
limit and perform an SU(8) calculation that hints at new states based on closed
strings in higher representations.
