Over the past century, two introduced Eurasian trees, saltcedar (Tamarix spp.) and Russian olive (Elaeagnus angustifolia) have become wide spread on western United States of American (U.S.) rivers. This paper reviews the literature on the following five key areas related to their distribution and abundance in the western United States: (1) the history of introduction, planting, and spread of saltcedar and Russian olive; (2) their current distribution; (3) their current abundance; (4) factors controlling their current distribution and abundance; and (5) models that have been developed to predict their future distribution and abundance. Saltcedar and Russian olive are now the third and fourth most frequently occurring woody riparian plants and the second and fifth most abundant species (out of 42 native and non-native species) along rivers in the western United States. Currently there is not a precise estimate of the areas that these species occupy in the entire West. Climatic variables are important determinants of their distribution and abundance. For example, saltcedar is limited by its sensitivity to hard freezes, whereas Russian olive appears to have a chilling requirement for bud break and seed germination, and can presumably survive colder winter temperatures. Either species can be dominant, co-dominant or sub-dominant relative to native species on a given river system. A number of environmental factors such as water availability, soil salinity, degree of stream flow regulation, and fire frequency can influence the abundance of these species relative to native species. Numerous studies suggest that both species have spread on western rivers primarily through a replacement process, whereby stress-tolerant species have moved into expanded niches that are no longer suitable for mesic native pioneer species. Better maps of current distribution and rigorous monitoring of distributional changes though time can help to resolve differences in predictions of potential future spread. An adequate understanding does not yet exist of what fraction of western riparian zones is resistant to dominance by either of these species, what fraction is at risk and could benefit from intervention, and what fraction has been altered to the point that saltcedar or Russian olive are most likely to thrive.