Months later, she was delighted to discover a mobile Web browser, Mobicip — designed for devices like the iPod Touch, iPhone, iPad and Android OS-based devices like the Kindle Fire — that is easy to set up quickly and blocks content either by age or by categories like pornography, chat or games.

Sometimes danger lurks where parents don’t expect it. Jeanne Sager, a blogger, assumed it was safe to let her 6-year-old daughter, Jillian, watch “My Little Pony” videos. But when she left the room for a moment, she heard something that didn’t sound anything like a cartoon.

Her daughter had stumbled upon a graphic video by clicking on a related link listed to the right of the video player. It is one of the most common complaints of parents who discover that their children have been exposed to sexually explicit material online — that a few clicks on YouTube can land a child in unexpected territory, like a subgenre of pornography where popular cartoon characters, like Batman or Mario Bros., are dubbed over with alternate soundtracks and editing to show the characters engaging in explicit acts.

In this case, Ms. Sager simply told her daughter, “There are some videos we shouldn’t be watching,” and made sure she knew she hadn’t done anything wrong. Later, she set up a separate computer login for her daughter, with bookmarks to her favorite sites, and no YouTube allowed.

For J. Carlos, a writer from Pasadena, Calif., who also asked that his last name not be used, the need for the pornography conversation emerged when he and his 14-year-old son were hiking in the mountains of Virginia. While borrowing his son’s smartphone to look for a restaurant, he noticed the search history, he said, and immediately realized, “Oh, O.K., it’s time to have that conversation.”

He wished they’d had it earlier, he said. The search terms that popped up seemed both naïve and potentially troublesome, and he worried that his son might unintentionally violate child-pornography laws by looking for images of girls his own age.

But the conversation that followed was, according to sex educators to whom it was recounted, an ideal response.