Wal-Mart's world-leading status has been built primarily on its dominance of its home market, and the group in fact has very few international operations (it is present in just nine other countries), with only the Mexican (Walmex) and British (Asda) units of any real size and importance.
But recent moves into the Brazilian market, where it acquired the majority of Ahold's business, strengthened its hand in Latin America (it is also present in Argentina), and the group is also thought to be one of several looking to expand its Chinese operations following the recent relaxation of investment regulations there.
But Europe has traditionally been a weak point in the Wal-Mart chain, notwithstanding the success of Asda, now the UK's second-largest grocer after Tesco. Indeed, the US group's only other European operations are in Germany, where it currently runs around 90 Supercenters.
Part of the reason for Wal-Mart's lack of progress in Europe may be down to its particular trading format - although not technically a discounter, the group has always been a value operator, stocking a wide range of both food and non-food items, and this particular combination has never been particularly common in Europe.
But no doubt buoyed by the success of Asda - a 'best value' retailer performing very successfully in a market which has traditionally been one of the most upmarket in Europe - and by the rising power of the discount sector across the recession-hit Continent, Wal-Mart now appears ready to chance its arm in the wider European arena.
Speaking to the Financial Times newspaper this week, Wal-Mart's chief executive Lee Scott said that Asda could be the motor for growth throughout the rest of Europe, with the British fascia being potentially rolled out in other countries, a move which would heighten its rivalry with Tesco.
Scott told the paper that he could not think of any country where Wal-Mart would not like to do business, although he declined to be drawn on which particular countries were likely to be targeted first. He did say, however, that expansion would take the form of both acquisitions and new store developments.
But greenfield expansion into the crowded European market will not be easy, especially with Wal-Mart's large store formats. European planning regulations are already some of the toughest in the world, with restrictions on large store developments in key markets such as the UK, France, Germany and Spain, and acquisitions would certainly seem the most likely option in these countries.
Central and eastern Europe offers perhaps greater opportunity for the US group, not least because these are still very much value-driven markets. Hypermarkets have also been the format of choice for groups such as Carrefour, Tesco and Ahold looking to expand their operations there.
But there are few small supermarket operators left anywhere in Europe which would allow Wal-Mart to dip its toe in the market, and expansing via acqusition is likely to mean a major acquisition. With no large operations there, apart from the UK-only Asda group, Wal-Mart would be unlikely to meet any opposition to a takeover from competition authorities, but just finding a potential partner is likely to be its main problem.
Ahold's central and eastern European business would be the most obviosu choice, but that seems to be the one part of the Dutch group's business which it will not sell off (having already divested its Latin American and Asian units and put its Spanish arm up for sale).
Apart from that, and concentrating on hypermarket operators which fit Wal-Mart's requirements, few other names spring to mind. French groups such as Casino or Auchan are too closely held, while most of Spain's major players (Eroski apart) are French owned and German discounters such as Aldi or Lidl are too powerful.
Smaller players such as Delhaize or Jeronimo Martins could be potential takeover targets, however.