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Natural rafting is an easy, non‐evidence‐based solution often used to explain the presence of a variety of species on isolated islands. The question arises as to whether this solution is based on solid scientific grounds. It is a plausible colonisation route only if intricate networks of variables are considered and many different conditions satisfied. This review provides a descriptive account of some of the most critical issues underlying the theory of natural rafting that should be addressed by its supporters. These include: (i) biological variables; (ii) characteristics of the vessels; and (iii) physical variables. Natural rafting may explain the dispersal of poikilotherms with low metabolic rates and low resource requirements that could withstand trans‐oceanic crossings, but explaining the transport of homeothermic terrestrial mammals to oceanic islands is more problematic. Drifting at sea exposes organisms to high concentrations of salt, high temperature and humidity excursions, starvation, and above all to dehydration. A sufficiently large group of healthy reproductive individuals of the two sexes should either be transported together, or be able to reassemble after separate crossings, to prevent inbreeding, genetic drift and ultimately extinction. Any vessels of flotsam occupied must minimally provide the animals they transport with sufficient provisions to survive the journey, offer minimum friction and drag through water, and be transported by appropriately directed, sustained, high‐speed currents. Thus, a 'sweepstakes colonisation' event would be the result of a lucky combination of all, or at least the majority, of these factors. Some cases throw doubt on the use of a natural rafting model to explain known animal colonisations, with one of the most striking examples being Madagascar. This island is far from the nearest mainland coasts and the sea currents in the Mozambique Channel are directed towards Africa rather than Madagascar, yet, the island was colonised by terrestrial mammals (e.g. extinct hippopotamuses, lemurs, carnivores, rodents and tenrecs) unable to swim and to survive long journeys at sea. In order to assess the feasibility of the natural rafting model in a case such as Madagascar, tests were performed using three variables for which enough information could be obtained from the literature: length of survival without food, survival without water, and sea current speed. The distributions of these variables appear to be log‐normal and multiplicative, or follow a power‐law, rather than being Gaussian. The tests suggest that a distributional analysis is a more suitable approach than the use of geometric probability to calculate the probabilities associated with the examined data. Such non‐linear and self‐organising systems may reach a critical point governed by different competing factors. Mammals with high survival requirements, such as lemurs and hippopotamuses, thus may have a virtually zero probability of reaching distant islands by natural rafting. Our results raise doubts as to the validity of a natural rafting model, and we urge a rethinking of the modes in which numerous islands were colonised by land mammals and a careful revision of past geological and phylogeographic work. [ABSTRACT FROM AUTHOR]