Until the morning of April 24, 2013, director Andrew Morgan hadn’t really given much thought to the topic of fashion. But as he grabbed a coffee and a copy of the New York Times that day, he read about the collapse of the Rana Plaza garment-factory building, which killed more than 1,100 people and injured some 3,000 more.

“It definitely broke my heart, but I think the more stunning thing to me when I read that article was the awareness that I had never in my whole life really stopped to think about where my clothes came from,” Mr. Morgan said. “I grew up in middle America, middle class, and I had never stopped to think about the fact that some of my really simple choices might have very real impact on the world.”

Mr. Morgan immediately started researching the topic and talking to people around the world, and by the end of the week, he decided to make a film. A Kickstarter campaign and two years later, “The True Cost,” a documentary examining the environmental, social and even the psychological impact of our rapid consumption of fashion, opens today in Los Angeles, New York and London, as well as on iTunes and video on-demand services.

The film represents Mr. Morgan's own journey of discovery as he documented fashion's globalized supply chain—whether it is discussing pesticide usage on a Texas cotton farm, meeting women in Bangladesh who are struggling to create a better way of life for their children, or examining a fair-trade brand's process in Japan.

He talked with Speakeasy by phone from London to discuss fair trade, Brooklyn and why donating your clothing isn't helping the problem.