The invasive alga Sargassum muticum has recently been reported in the Firth of Lorn, west coast of Scotland. This represents the first sighting of the species north of the Kintyre Peninsula, a land barrier that had been expected to slow the northwards spread of S. muticum. This paper presents a thorough review of literature concerning the dispersal and establishment of this invasive alga and predicts potential dispersal trajectories and likely areas for future establishment in Scotland. From previous dispersal rates, S. muticum is likely to spread throughout the west coast of Scotland in the next few years, predominantly via natural pathways although anthropogenic vectors may also contribute to dispersal. Sheltered and moderately exposed sea lochs and shorelines, on the west coast of Scotland in particular, are likely to provide favourable conditions for the establishment of persistent populations of S. muticum. Conditions on the north and east coasts of Scotland were considered less favourable, both for the dispersal and establishment of S. muticum. The spread of S. muticum is unlikely to cause serious widespread ecological impacts, however, it does have the potential to cause economic damage to the aquaculture industry which is a major employer on the west coast of Scotland. The establishment of dense highly visible canopies would also constitute a degradation of the natural heritage value of Scottish shorelines. It would be prudent to investigate means of preventing persistent populations from establishing in areas of economic importance or with high natural heritage value.