Heterogeneity in pathogen transmission is investigated in stochastic multigroup models, with one group representing superspreaders. Superspreaders are characterized as those individuals able to infect a disproportionately high number of susceptible individuals. Recent emerging diseases such as SARS, MERS and Ebola are some examples of outbreaks with superspreading events. We apply continuous-time Markov chains and branching process theory to determine estimates for the probability of a minor or a major epidemic when initiated by a either a superspreader or a non-superspreader. We also examine the time until the outbreak is observed and discuss some applications to emerging and zoonotic infectious diseases.