The shoes are so recognizable that you know the brand when you see them: Smooth, rounded tops with rubber soles and a stripe that wraps around them. They're Converse's Chuck Taylor's, of course, the inexpensive, durable shoes that have been favorites in the United States for decades.

At least, that's what Converse is betting. On Tuesday Nike, who owns the All Star brand, brought a lawsuit against 31 different companies—including WalMart and Sketchers—which it claims have appropriated elements of Chuck Taylor's classic design. The suit was filed in U.S. District Court in New York. Nike is also filing a separate complaint with the International Trade Commission to prevent competitors from importing the so-called "imposters" into the U.S.

Typically, shoe companies go after knockoffs because of price undercutting. Chuck Taylor's, though, are relatively cheap: Zappos sells them for just $44.95, while Google Shopping shows prices even lower. A new Air Jordan can set you back $150, if not double. On top of that, Converse sales make up just 6 percent of Nike's overall sales, according to The New York Times, or about $1.7 billion of the company's $28 billion. But the "world's largest sporting-goods company" is not just in the business of selling running shoes, they are increasingly selling fashionable items to wear every day.