A year after U.S. authorities closed Backpage.com, the biggest player in the online sex-for-sale industry, investigators are focused on three websites now dominant in the American market and the Swiss businessman who they believe may control them.

U.S. authorities, including the Department of Homeland Security and the Justice Department, are investigating whether the sites have engaged in or knowingly enabled human trafficking, prostitution and money-laundering, and what ties they may have with David Azzato, according to people familiar with the matter. Mr. Azzato was convicted in France in 2011 of profiting from prostitution through a European network of escort-ad sites.

The websites in the years-long U.S. investigation all make their money from escort advertisements or posting user-generated reviews of sex-related services.

They include Rubmaps.ch, a massage-parlor review site that recently replaced Rubmaps.com. Florida authorities cited Rubmaps.com when seeking a warrant to search a spa allegedly selling sexual services in a case that entangled New England Patriots owner Robert Kraft, who in February pleaded not guilty to soliciting prostitution. The others are EroticMonkey.ch, which offers escort reviews contributed by customers, and Eros.com, an escort-advertising site.

Among websites in the underground commercial sex economy in the U.S., Eros.com was the most visited ad platform in July, according to an analysis of visitor data compiled by Alexa Internet Inc. Rubmaps and EroticMonkey were the two most visited review sites that month, according to ChildSafe.ai, which performed the analysis and provides data and other tools to help law enforcement combat sex trafficking.