Among luxury companies, conventional wisdom used to be that participation in e-commerce—and, in particular, selling through multibrand retail websites—was only for the lower and middle range of products. The pervasive belief was that luxury shoppers, with their discriminating taste and preference for high-priced goods, wouldn’t buy expensive things online; they would always opt for the personalized customer service and tactile shopping experience that monobrand brick-and-mortar stores provide.

That thinking has evolved in recent years. The success of ventures such as Net-A-Porter has shown that consumers are indeed willing to buy luxury products online, and at undiscounted prices. One telling statistic: while overall sales of luxury goods grew by a mere 2 percent in 2013, online luxury sales increased by 20 percent to an estimated €9 billion. We believe this growth will continue; we project that sales of luxury goods online will more than double to approximately €20 billion in the next five years.

Today e-commerce represents a scant 4 percent of luxury sales—but e-commerce is only one aspect of the digital opportunity. Our research found that an additional 40 percent of luxury purchases are in some way influenced by consumers’ digital experience—for example, through online research of an item that is subsequently bought offline, or social-media “buzz” that leads to an in-store purchase.

Given the undeniable and growing power of the digital universe, all luxury brands must think hard about their digital presence. The “right” digital strategy differs for every brand, but what’s certain is that it’s no longer just about a beautifully designed and user-friendly website or effective banner ads. The most successful luxury brands will be those that build a compelling mobile presence, engage and influence consumers through targeted use of social media, and focus on a carefully chosen set of digital-performance metrics.