| Spreading of infective agents like pathogens, computer viruses, fashions, or political opinions can exhibit a percolation transition that separates small outbreaks from giant ones which reach a non-zero fraction of the population. Typically, such transitions are continuous (“second order”), but recently discontinuous (“first order”) transitions (DT's) have aroused huge interest. We discuss models involving cooperativity, either between two different types of spreading agents or between "attacking" neighbors. We show that either mechanism can lead to DT’s or to continuous ones, depending on the chosen order parameter, the topology of the underlying network, and on seemingly minor details of the implementation. Moreover, all DT's are also accompanied by various non-trivial power laws, which blurs the fundamental distinction between first and second order transitions. |