Non-native species are plants or animals that not belong here naturally, and could not get here, or survive on their own.
Non-natives are imported, sometimes as exotic specialties, curio or houseplant, home or hunting animals, such as e.g. the rabbit in Australia.
Some managed to escape, others were introduced to 'enrich' the area, or because once small and gentle animals became large, dangerous or annoying (in the house).
Seeds, insects and small animals sometimes travel along in freight of ship (hold)s.
Water residents sometimes make long trips in the ballast water (to stabilize a ship without cargo) on intercontinental transport.
Not all exotics are a problem. But due to lack of natural predators, they can threaten (parts of) their own flora and fauna. Also by parasites and diseases they bring and to which native species are not resistant. And the fact that they compete with the own residents to the same food. The biotope is disrupt, the balance is disturbed and biodiversity decreases. Threatening species we call invasive.
The degeneration of domesticated species like deer, cat, pigeon is a similar problem.
Species that migrated on their own are not included to non-native: collared dove, chestnut trees.
Peak times for the supply of new species were the Crusades entering spices and weed seeds (such as poppy and cornflower) and the period after 1492 with the importation of plants from the New World. Useful newcomers like potatoes, corn, tomato I hear but rarely mention as non-native.
Non-natives in the Low Countries:
American mink (Neovison vison), Asian hornet (Vespa velutina nigrithorax)
coypu or nutria (Myocastor coypus), Canada Goose (Branta canadensis), Chinese mitten crab (Eriocheir sinensis), pheasant (Phasianus colchicus), rose-ringed parakeet (Psittacula krameri), sacred ibis (Threskiornis aethiopicus), muskrat (Ondatra zibethicus), Egyptian Goose (Alopochen aegyptiaca), Pallas's squirrel or red-bellied squirrel (Callosciurus erythraeus), red-eared slider (turtle ) (Trachemys scripta elegans), ruddy duck (Oxyura jamaicensis), bull frog (Rana catesbeiana), raccoon (Procyon lotor), raccoon dog (Nyctereutes procyonoides)
(fish) Stone moroko (Pseudorasbora parva), American signal crayfish (Pacifastacus leniusculus), Chinese mitten crab (Eriocheir sinensis), zebra mussel (Dreissena polymorpha), grass carp (Ctenopharyngodon idellia), pumpkinseed (Lepomis gibbosus)
Horse chestnut leaf miner (Cameraria ohridella), Asian ladybeetle (Harmonia axyridis)
The Chinese muntjac (Muntiacus reevesi) with a shoulder height of just 50cm is a small deer with striking tusks that has been spotted since 2005 in Flanders, especially in Brasschaat and Schoten. The species threatens local biodiversity. In Great Britain where a number of Reeves' muntjac have escaped from a zoo in 1930, 130,000 of them are already roaming around.
Plants
Ragweed (Ambrosia artemisiifolia), red oak (Quercus rubra), black cherry (Prunus serotina), Douglas Fir (Pseudotsuga menziesii), floating pennywort (Hydrocotyle ranunculoides), tree of heaven (Ailanthus altissima), Japanese knotweed (Fallopia japonica, syn Polygonum cuspidatum), parrot feather herb (Myriophyllum aquaticum, M. brasiliense), Himalayan balsam or policeman’s helmet (Impatiens glandulifera), giant hogweed (Heracleum mantegazzianum (the hairs are dangerous)), African elodea, curly waterweed or oxygen weed (Lagarosiphon major), New Zealand pigmy weed (Crassula helmsii), water primrose (Ludwigia grandiflora, L.uruguayensis, Jussiaea repens)).