The paper Zermelo 1896a contains what is commonly called the recurrence objection (Umkehreinwand) to Ludwig Boltzmann's approach to statistical physics. It gave rise to a heated dispute with Boltzmann, a controversy comprising the four papers reprinted here. The dispute has often been commented on, both from a historical and from a philosophical foundations of physics perspective. In the popular literature, a picture has been painted in which Boltzmann has the upper hand and Zermelo's objections are described as hostile, misguided, or wrongheaded. However, Zermelo has the better arguments in this debate. His objections are stated fairly and precisely. Boltzmann's responses fail to answer or fully elucidate his position on the questions Zermelo is asking. This view does not deny the fact that in the early decades of the 20th century, Boltzmann's mechanistic-atomistic approach gained a clear victory. Nonetheless, a generally accepted answer to the question of how to explain irreversible phenomena in statistical physics has not been reached.