This is the first in a series of status reports on the 1100 open problems listed in the book “Open Problems in Topology” (1990; see the preceding review), edited by the authors. For the next few years, “Topology and its Applications” will publish such status reports at regular intervals. Our goal is to give a brief account of problems solved, by whom, and whether preprints are available. Already more than twenty solutions have been announced. In addition to announcements of new solutions, these reports will contain a matrix of problem numbers updated to indicate those problems still open. In this manner, we hope to fulfill our initial ambition to provide a source book of current open problems.