It’s the next jump in resolution after HD, but 4K (or UHD, which is about 3.8K) presents challenges when it comes to content and technology.
Besides the question of whether a person can tell the difference, i.e. a real, perceptual improvement in resolution---see Phil Plait's article on arcminutes and 4K TV---there are two main problems with the distribution of 4K films: 1) Acquisition, and 2) Visual Effects.
Let's deal with the acquisition question first.
Movies have to be shot in an ultra-high-definition format in order to be 4K. There aren't enough 4K films in existence to put together a library of any consequence.
When movies originate on film, each frame of film is scanned at a certain resolution, like 2K, 4K, or even 8K---whichever is deemed adequate by the production company or studio, and 35mm film is an ultra-high-def format.
But most movies aren't shot on film anymore, so they can't arbitrarily be scanned. Instead, their resolutions are dependent on the digital systems used for acquisition; these camera systems usually have a resolution of about 2K or 3K.
To screen in 4K, digitally-captured movies are often scaled up to a 4,096-pixel master or simply mastered in 2K (2,048 pixels across). A few films, such as Girl with the Dragon Tattoo, were shot and mastered at higher resolutions like 4,352 × 2,176, but they extracted from that master a final frame size of 3,600 x 1,500 pixels, still less than 4K.
But even movies shot on film haven't traditionally gotten the 4K treatment. Lord of the Rings: Fellowship of the Ring was shot on 35mm film (Super 35), scanned for a digital intermediate, and mastered in 2K---but since each frame is a 2.40:1 widescreen extraction, its final, mastered resolution was 2,048 x 854, which is only 2K and vertically much fewer pixels than even full-HD.
Twenty years ago, before digital cinema cameras were commonplace, there was another form of digital origination starting to emerge: rendering the entire film within the computer.
Toy Story was the first all-digital 3D animated movie, and it was rendered at less than 2K---only 1,536 x 960 pixels.
Let’s turn to the second issue: visual effects. Even for movies that have 4K masters, almost none of the effects are in 4K. Current estimates suggest that visual effects are rendered in full 4K for less than 5% of films; the vast majority of films render VFX in 2K.
Multiple reasons are behind this fact: time, cost, bandwidth, even the textures in the VFX CG models themselves which would need to be made at higher resolutions to render correctly in 4K.
One aside on color: UHD specs recommend a 10-bit color gamut (30-bit color total, compared to traditional 24-bit color distribution formats). And wider color gamuts mean larger amounts of data. A UHD frame is four times the data in pixels, but it's also 25% more data in terms of color-depth.
An example: one uncompressed frame of 10-bit UHD is 31.1 MB (3840 x 2160 x 3.75 Bytes), compared with 6.2 MB per 8-bit HD frame (1920 x 1080 x 3 Bytes).
5x the data
31.1 MB/frame vs. 6.2 MB/frame
_____________
So, UHD is about 5 times more data than HD---even if they're compressed using similar codecs. And if the UHD compression schemes are able to be twice as efficient as those used in HD, there will still be a challenge in distributing 2.5 times the data; bandwidth alone will be an issue, as it has already started to be for subscribers of some streaming UHD services like Amazon and YouTube.
After all of these issues are taken into account, the upshot is that 20 years' worth of cinema (from the '90s to the '10s) are in 2K or less than 2K, and they always will be so. Their content will be scaled up to fit the screen, and even brand-new movies will incorporate 2K effects inside of 4K-acquired content.
A final note: From the way 4K TVs are advertised, you'd think there would be plenty of content for them. We know that this isn’t true in terms of films. Sometimes, 4K TVs are targeted to gamers, as in this recent ad from Best Buy:
Best Buy would have you believe that the XBox One supports gameplay at 4K; it doesn't.
Graphics from the games are scaled up from HD to 4K—and in that case, what's the point of a 4K display? This situation is like buying a new car: you've got a huge, V8 engine, but your fuel line can only supply enough gasoline for four cylinders, leaving the remaining four motionless.
Unfortunately, for both films and games, this kind of fuel starvation is what we're seeing in the 4K world.
IBC: 4K and better pixels
Why Buying A 4K TV Right Now Is A Waste Of Money
4K on the Cheap: Ultra HD TV Is Almost Ready for Mainstream
4K TVs Are Forked. You Should Wait Before You Buy One