Plastic debris constitutes up to 87% of marine litter and represents one of the most frequently studied vectors for marine alien species with invasive potential in the last 15 years. This review addresses an integrated analysis of the different factors involved in the impact of plastic as a vector for the dispersal of marine species. The sources of entry of plastic materials into the ocean are identified as well as how they move between different habitats affecting each trophic level and producing hot spots of plastic accumulation in the ocean. The characterization of plastic as a dispersal vector for marine species has provided information about the inherent properties of plastics which have led to its impact on the ocean: persistence, buoyancy, and variety in terms of chemical composition, all of which facilitate colonization by macro and microscopic species along with its dispersion throughout different oceans and ecosystems. The study of the differences in the biocolonization of plastic debris according to its chemical composition provided fundamental information regarding the invasion process mediated by plastic, and highlighted gaps of knowledge about this process. A wide range of species attached to plastic materials has been documented and the most recurrent phyla found on plastic have been identified from potentially invasive macrofauna to toxic microorganisms, which are capable of causing great damage in places far away from their origin. Plastic seems to be more efficient than the natural oceanic rafts carrying taxa such as Arthropoda, Annelida, and Mollusca. Although the differential colonization of different plastic polymers is not clear, the chemical composition might determine the community of microorganisms, where we can find both pathogens and virulent and antibiotic resistance genes. The properties of plastic allow it to be widely dispersed in practically all ocean compartments, making this material an effective means of transport for many species that could become invasive.