Google Play Music just added podcast support recently, but Stitcher has been successfully indexing and streaming podcasts for years. This has not gone unnoticed. Stitcher has been acquired from owner Deezer for $4.5 million. The buyer is E.W. Scripps, which probably isn't a name with which you're familiar. You may be familiar with what they do, though.
According to The Wall Street Journal, Stitcher will operate under E.W. Scripps' Midroll Media unit. Midroll's business is selling ads in podcasts. It handles ads for shows like WTF with Marc Maron and The Nerdist. Midroll admits that this acquisition is connected to the company's plans for a premium service called Howl that features ad-free archives of popular shows for $5 per month. Stitcher might be very useful in that venture.
For the time being, Stitcher will continue operating as it always has. I wouldn't expect any huge alterations to Stitcher's formula. Maybe just some new things grafted on.