In this paper, the challenges in simulation of tsunami-induced currents are reviewed. Examples of tsunami dynamics in harbors, overland flow, and through urban environments are presented, with a focus on the numerical and natural variability in speed predictions. The discussion is largely aimed to show that high-confidence prediction of location-specific currents with a deterministic approach should not be possible in many cases. It is recommended that the tsunami community should look to some type of stochastic approach for current hazard modeling, whether that be a community-wide ensemble approach or a stochastic re-formation of our hydrodynamic theories. Until such tools are available, existing deterministic simulations of tsunami-induced currents require a high level of expert judgement in the analysis, presentation, and usage of model output.