We consider some mathematical models in one-dimensional advective environments. Individuals are exposed to unidirectional flow, with the possibility of being lost through the boundary. Our analysis suggests that, in contrast to the case of no advection, slow dispersal is generally selected against in advective environments. When the diffusion and advection rates are small and comparable, we determine some criterion for the existence and multiplicity of evolutionarily stable strategies. We also study whether that these strategies are convergent stable. This talk is based on joint works with King Yeung Lam, Frithjof Lutscher, Peng Zhou.