2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/58498This expository article, intended to be accessible to students, surveys results about the presence or absence of zeroes of the Bergman kernel function of a bounded domain in C^n. Six open problems are stated. The article is based on a lecture at the third Korean several complex variables symposium held at the Global Analysis Research Center at Seoul National University in December 1998.14 pages; to appear in the Journal of the Korean Mathematical SocietyComplex Variables32H10text