The Late Babylonian Astronomical Diaries and related texts contain a large body of records of astronomical phenomena which were carefully and systematically observed between about 600 BC and 50 BC. Most of these observations are of regular (cyclical) astronomical phenomena such as passages of the planets past certain stars, the first and last appearances, stations, and acronychal risings of the planets, and eclipses of the sun and moon. However, a smaller number of observations of irregular, transient astronomical phenomena were also recorded.In addition to being of historical interest, records of certain transient phenomena have applications in modern science. In this paper, we provide a catalog of three types of transient phenomena observed by the Babylonians -haloes, meteors, and comets -as well as some basic analysis of the records and the necessary contextual information to facilitate their analysis and use by other scholars.