  Some past and ongoing explorations of the spectrum of QCD using Monte Carlo
simulations on a space-time lattice are described. Glueball masses in the
pure-gauge theory are reviewed, and the energies of gluonic excitations in the
presence of a static quark-antiquark pair are discussed. Current efforts to
compute the baryon spectrum using extended three-quark operators are also
presented, emphasizing the need to use irreducible representations of the cubic
point group to identify spin quantum numbers in the continuum limit.
