Although many species shift their phenology with climate change, species vary significantly in the direction and magnitude of these responses (i.e., phenological sensitivity). Studies increasingly detect early phenology or high phenological sensitivity to climate in non-native species, which may favor non-native species over natives in warming climates. Yet relatively few studies explicitly compare phenological responses to climate between native vs. non-native species or between non-native populations in the native vs. introduced range, limiting our ability to quantify the role of phenology in invasion success. Here, we review the empirical evidence for and against differences in phenology and phenological sensitivity to climate in both native vs. non-native species and native and introduced populations of non-native species. Contrary to common assumptions, native and non-native plant species did not consistently differ in mean phenology or phenological sensitivity. However, non-native plant species were often either just as or more sensitive, but rarely less sensitive, to climate as natives. Introduced populations of non-native plant species often show earlier reproduction than native populations of the same species, but there was mixed evidence for differences in phenological sensitivity between introduced and native plant populations. We found very few studies comparing native vs. invasive animal phenology. Future work should characterize phenological sensitivity to climate in native vs. non-native plant and animal species, in native vs. introduced populations of non-native species, and across different stages of invasion, and should carefully consider how differences in phenology might promote invasion success or disadvantage native species under climate change.