'Forward models' are increasingly recognized as a crucial explanatory concept in vertebrate motor control. The essential idea is that an important function implemented by nervous systems is prediction of the sensory consequences of action. This is often associated with higher cognitive capabilities; however, many of the purposes forward models are thought to have analogues in insect behaviour, and the concept is closely connected to those of 'efference copy' and 'corollary discharge'. This article considers recent evidence from invertebrates that demonstrates the predictive modulation of sensory processes by motor output, and discusses to what extent this supports the conclusion that insect nervous systems also implement forward models. Several promising directions for further research are outlined.