Ever since Amazon.com Inc. (NASDAQ: AMZN) announced its offer to buy Whole Foods Market Inc. (NASDAQ: WFM), a lot of attention has been focused on shopping online for groceries. Who shops for groceries online? What do they buy? Which online stores are most popular?

E-commerce marketing research firm eMarketer recently found that U.S. consumers across all age groups are getting their groceries from online-only stores but the most active shoppers are millennials. The researchers cite a recent survey that 43% of millennial respondents shop at least occasionally for groceries online, a rate that is 80% higher than it was just two years ago.

GenX respondents shop at online-only grocers at about half that rate, and older Americans are the least likely to buy groceries at online-only stores.

eMarketer noted:

While multiple generations have taken to buying groceries online, shopping with online-only retailers for these items at such a high rate is unique to millennials. Moreover, the survey found that the number of millennials buying groceries almost exclusively from online-only retailers has risen significantly.

The primary driver for consumer acceptance of online grocery shopping is convenience, cited by 60% to 78% of all consumer age groups surveyed. Interestingly, more than half of respondents to a recent TrendSource survey said they prefer to order through a local grocer rather than buying through a vendor such as Amazon. The Amazon acquisition of Whole Foods can be viewed as a move into that local market.

What consumers purchase through online grocers are primarily dry goods, household items and cleaning supplies. Other often-purchased items include baby food and pet food. Fresh foods like meat, seafood, dairy and produce are typically avoided, even by millennials.

How big a threat is this trend toward more online grocery shopping to big-box stores like Wal-Mart Stores Inc. (NYSE: WMT) and Target Corp. (NYSE: TGT) and traditional grocers like Safeway and Kroger Co. (NYSE: KR)? Another survey, this one by Progressive Grocer, found that 25% of Walmart.com shoppers buy fresh foods from the site compared with 10% who buy from Target.com, 8% who make purchases at Walmart’s Jet.com and just 5% who buy from Amazon Fresh.

Walmart’s ubiquity and free pickup make a potent pairing. Chris Medenwald of market research firm Field Agent said:

Perhaps this will change as Amazon makes further inroads into [brick-and-mortar] retail [with the purchase of Whole Foods], but, for now, Walmart.com enjoys tremendous omnichannel leverage – which is especially important in the grocery category. With Walmart.com, shoppers enjoy the convenience of online shopping alongside the fresh appeal and immediate gratification of brick-and-mortar retrieval. So, while in shoppers’ minds, Amazon currently excels Walmart.com in many categories, Walmart’s advantage in the fresh grocery space feels like a strategy to really build on. … The combination of fresh grocery with store tie-ins is one place Walmart – and Jet – can really apply pressure to Amazon, though the clock may be ticking.

But how does Walmart do among millennials, the group leading the charge into online grocery shopping? According to another recent survey sponsored by publisher Condé Nast and investment bank Goldman Sachs, Walmart does quite well with these young consumers. Walmart and Target are cited by 43% and 42% of millennials as their most favored shopping destinations.

Amazon was cited by 17% of millennials as a favorite food retailer, but that number is expected to rise as a result of the Whole Foods deal. The top 10 favorite food retailers, brick-and-mortar as well as online, cited by the cross-generational national sample are Walmart (35%), Costco (34%), Trader Joe’s (33%), Whole Foods (32%), Target (25%), Kroger (19%), Safeway (16%), Aldi (15%), Sam’s Club (13%) and Amazon (12%).

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