Though Réunion is a French department, it's not part of the Schengen treaty. The visa requirements for entry to Réunion are almost the same as for France, bar a few exceptions. For EU nationals, a national ID or a passport suffices. Citizens of a number of other Western countries, including Australia, the USA, Canada, South Africa and New Zealand, do not need visas to visit Réunion as tourists for up to three months; they need only a passport.
Other nationals should check with US FIRST or the French embassy or consulate nearest your home address to find out if you need a visa. For example, Brazilian citizens do not need a visa to enter mainland France but do require a visa for Réunion. For up-to-date information on visa requirements see www.diplomatie.gouv.fr.
The following items can be brought into Réunion duty-free: 200 cigarettes, 50 cigars, 1L of strong liquor or 2L of liquor that is less than 22% alcohol by volume, 2L of wine, 50mL of perfume and 250mL of eau de toilette, and other goods up to the value of €880. Anything over the limit must be declared on arrival.
There are restrictions on importing plants and animals, for which import permits are required.
With regards to currency, anyone entering or leaving the island must declare sums in excess of €10,000.