It is now 130 years since Fritz Müller proposed an evolutionary explanation for the close similarity of co-existing unpalatable prey species, a phenomenon now known as Müllerian mimicry. Müller's hypothesis was that unpalatable species evolve a similar appearance to reduce the mortality involved in training predators to avoid them, and he backed up his arguments with a mathematical model in which predators attack a fixed number (n) of each distinct unpalatable type in a given season before avoiding them. Here, I review what has since been discovered about Müllerian mimicry and consider in particular its relationship to other forms of mimicry. Müller's specific model of associative learning involving a "fixed n" in a given season has not been supported, and several experiments now suggest that two distinct unpalatable prey types may be just as easy to learn to avoid as one. Nevertheless, Müller's general insight that novel unpalatable forms have higher mortality than common unpalatable forms as a result of predation has been well supported by field experiments. From its inception, there has been a heated debate over the nature of the relationship between Müllerian co-mimics that differ in their level of defence. There is now a growing awareness that this relationship can be mediated by many factors, including synergistic effects between co-mimics that differ in their mode of defence, rates of generalisation among warning signals and concomitant changes in prey density as mimicry evolves. I highlight areas for future enquiry, including the possibility of Müllerian mimicry systems based on profitability rather than unprofitability and the co-evolution of defence.