Dozens of iPhone owners are taking Apple Inc. to court over the company’s disclosure that it slowed down old phones to preserve battery life, in what could become one of the biggest legal challenges to the smartphone since its 2007 debut.

Some five dozen iPhone customers have filed at least 59 separate lawsuits since December accusing Apple AAPL, +1.57% of slowing their phones to spur people to buy new iPhones, according to court records. The lawsuits were filed after Apple said in December that its software updates reduced the performance of older phone models. They seek an unspecified financial award, attorneys’ fees and free iPhone battery replacements, as well as a corrective advertising campaign.