It is often hoped that population genetics can answer questions about the demographic and geographic dynamics of recent biological invasions. Conversely, invasions with well-known histories are sometimes billed as opportunities to test methods of population genetic inference. In both cases, underappreciated limitations constrain the usefulness of genetic methods. The most significant is that humancaused invasions have occurred on historical timescales that are orders of magnitude smaller than the timescales of mutation and genetic drift for most multicellular organisms. Analyses based on the neutral theory of molecular evolution cannot resolve such rapid dynamics. Invasion histories cannot be reconstructed in the same way as biogeographic changes occurring over millenia. Analyses assuming equilibrium between mutation, drift, gene flow, and selection will rarely be applicable, and even methods designed for explicitly non-equilibrium questions often require longer timescales than the few generations of most invasions of current concern. We identified only a few population genetic questions that are tractable over such short timescales. These include comparison of alternative hypotheses for the geographic origin of an invasion, testing for bottlenecks, and hybridization between native and invasive species. When proposing population genetic analysis of a biological invasion, we recommend that biologists ask (i) whether the questions to be addressed will materially affect management practice or policy, and (ii) whether the proposed analyses can really be expected to address important population genetic questions. Despite our own enthusiasm for population genetic research, we conclude that genetic analysis of biological invasions is justified only under exceptional circumstances.