The defining feature of the eukaryotic cell, the nucleus, is bounded by a double envelope. This envelope and the nuclear pores within it play a critical role in separating the genome from the cytoplasm. It also presents cells with a challenge. How are cells to remodel the nuclear compartment boundary during mitosis without compromising nuclear function? In the two billion years since the emergence of the first cells with a nucleus, eukaryotes have evolved a range of strategies to do this. At one extreme, the nucleus is disassembled upon entry into mitosis and then reassembled anew in the two daughter cells. At the other, cells maintain an intact nuclear compartment boundary throughout the division process. In this review, we discuss common features of the division process that underpin remodelling mechanisms, the topological challenges involved and speculate on the selective pressures that may drive the evolution of distinct modes of division.