Turbulence in a superfluid differs from that in a classical fluid because the flow of a superfluid is strongly influenced by quantum effects. Such turbulence is therefore often described as quantum turbulence. We give a brief historical account of the study of quantum turbulence, explaining how our understanding of it has developed. Particular attention is then paid to developments during the past ten years, which have seen the study of types of quantum turbulence that have close classical analogues. Similarities and differences between the classical and quantum cases are discussed, and aspects that are either not understood or the subject of speculation are emphasized. The paper provides an introduction to other and more detailed presentations in the Symposium.