Populations are introduced into novel environments in different contexts, one being the biological control of pests. Despite intense efforts, less than half introduced biological control agents establish. Among the possible approaches to improve biological control, one is to better understand the processes that underpin introductions and contribute to ecological and evolutionary success. In this perspective, we first review the demographic and genetic processes at play in small populations, be they stochastic or deterministic. We discuss the theoretical outcomes of these different processes with respect to individual fitness, population growth rate, and establishment probability. Predicted outcomes differ subtly in some cases, but enough so that the evaluating results of introductions have the potential to reveal which processes play important roles in introduced populations. Second, we attempt to link the theory we have discussed with empirical data from biological control introductions. A main result is that there are few available data, but we nonetheless report on an increasing number of well-designed, theory-driven, experimental approaches. Combining demography and genetics from both theoretical and empirical perspectives highlights novel and exciting avenues for research on the biology of small, introduced populations, and great potential for improving both our understanding and practice of biological control.