As of now there are only a very few ways to enjoy 4K content as Amazon, Netflix, & YouTube are the only real ways. Thanks to the Blu-Ray Disc Association, there will be an alternative for 4K streaming via physical media called Ultra HD Blu-Ray.
The new format will support up to 3840 x 2160 resolution up to 60fps, high dynamic range, and expand the color range for all media. This will also support immersive sound formats like Dolby Atmos & DTS:X. If you thought Blu-Ray held a lot of storage, this new medium requires up to 66GB of data on a dual-layer disc and 100GB on a triple-layer disc. So trying to download movies form these things will definitely requires more storage on your computer or possibly a faster CPU/motherboard.
Licensing is set to start this summer as we can expect backward compatible UHD Blu-Ray players to go on sale sometime later this year.