The Showtime Anytime app has made its way to Apple TV

Showtime, the premium cable network known for “Dexter” and “Homeland,” has made it past Apple’s gates, with its on-demand videos of full episodes now available on the company’s video-streaming box Apple TV. The app is already available on Roku, which is known for its catalog of thousands of channels, and Amazon’s $99 Fire TV. The $99 Apple TV, which connects to televisions to stream video over the Internet, has been an afterthought in Apple’s device lineup. More than two years have passed without a hardware refresh to a new generation, limiting Apple TV’s recent updates to the addition of new channels, like AOL. Meanwhile, the growing popularity of streaming-media boxes has spurred a wave of competitors to emerge in the last year, including Fire TV and Google’s Chromecast. Apple’s gated approach to channel selection for Apple TV has kept its library of channels low, and some of the most enticing channels teased as coming to Apple TV — such as a Time Warner Cable appthat streams live channels from the cable provider over the Internet — have yet to appear.