There's no shortage of so-called devices – Roku 3, Apple TV, and PlayStation 4 – that bring Internet streaming of movies, TV, music, and more (also known as over-the-top content, or OTT) to your HDTV. For those of us who still need our cable TV to watch live sports, though, these turn into yet another box on the media credenza. Finding a replacement for your cableco's typically clunky set-top box, though, while delivering streaming video is a far tougher find. TiVo's new Roamio Pro does it with aplomb and has a features list that would boggle the mind of any dedicated tube watcher: It stores a massive 450 hours of HD recordings, can record six shows at once, includes a bevy of Web video services, and allows you to streams shows to iOS devices – whether you're at home or on the road.

While there are other DVRs, notably Dish's excellent Hopper, that offer similar specs, the Roamio goes beyond cable fare by fully integrating Web video (from Netflix, Amazon Instant Video, and Hulu Plus, among others) into its core functionality. For one, show recommendations include offerings from the full universe of entertainment options, not just what's on cable. So when you search for an episode of 'Sons of Anarchy,' you'll see availability for instant streaming on Netflix and Amazon as well as scheduled airings on FX.

Once equipped with a cablecard, which you'll need to order from your cable provider, the Roamio replaces your digital cable box and makes it possible for its six built-in TV tuners to start filling up its massive 3TB hard drive. Theoretically, it would take more than three days of constant recording on all six tuners to approach capacity, which means you'll likely never fill it. There's a sense of freedom that comes from not having to worry about when a show you recorded will be automatically deleted – bringing the modern joy of binge watching to prime time shows by letting a season's worth accumulate and brew for the next rainy day.

All those tuners come in handy if you take advantage of the Roamio's ability to add on TiVo Mini boxes ($100 a pop) that you connect to other TVs in your house (or to iOS devices, via a free app). Thus the Roamio becomes your whole-home DVR, making streaming to a different device nearly as simple as watching it through the Roamio directly. So, say you're in the office and want to catch a Bears game. Fire up the TiVo iOS app, select the game in the program guide, and the Roamio will record it – and can even stream it to you remotely. (Caveat: Some shows can't be streamed outside your home network because the rights owners have prohibited that feature).

Not surprisingly, all this freedom isn't exactly a bargain: The Roamio Pro runs $600 for the unit, plus a $15 monthly subscription. (If you don't need quite so much storage, the $400 Roamio Plus, with 150 hours of storage, might fit the bill.) For cord cutters who use an antenna, your only choice is the $200 basic Roamio, and satellite subscribers are out of luck because TiVo currently doesn't work with DirecTV or DISH. [$600 for unit, plus $15 monthly subscription; tivo.com]