We discuss several key problems of conventional QCD glueball sum rules in the spin-0 channels and show how they are overcome by nonperturbative Wilson coefficients. The nonperturbative contributions originate from direct instantons and, in the pseudoscalar channel, additionally from topological charge screening. The treatment of the direct-instanton sector is based on realistic instanton size distributions and renormalization at the operator scale. The resulting predictions for spin-0 glueball properties as well as their implications for experimental glueball searches are discussed.