I know close to nothing about VR. For me, at this point, VR just means doing smth like DrawLeftEye() and DrawRightEye(). Also, I'd guess screenspace techniques become too expensive due to higher res. That's all I know. So, my question: what are the differences, the new challenges that VR brings? Thx

Welcome to the awesome world of VR rendering! :) There's much to learn here, and I do have a character limit here, but I'll try my best to give a high-level overview of some things to watch out for.
I really like Alex's talk on VR rendering and the unique challenges VR presents. Check it out! http://alex.vlachos.com/graphics/Alex_Vlachos_Advanced_VR_Rendering_Performance_GDC2016.pdf I also spoke about this at a very high level here: https://www.youtube.com/watch?v=2-P1GzG8o54 , and at a slightly deeper level here: http://voicesofvr.com/464-the-graphics-pipeline-optimizing-vr-experiences-texture-compression-from-binomial/ .
So, you're right, we now have two views to draw. That alone presents its own problems. Most of the scene is the same in both eyes, it's just a slightly different perspective. It seems a total waste to just render the scene twice. How can we optimize this?
Remember that the eyes are also warped. You're no longer just looking at a nice, simple 2D rectangle 3 feet from your face. And a lot of graphics techniques relied on the fact that the screen was 2D-- the effects weren't actually volumetric, they were flat and restricted to a pass done on the whole screen. In VR, we want to create volumetric graphics techniques whenever possible and can't do the traditional screenspace effects.
Volumetric effects come up in more than just screenspace issues, too. When I was coding up high quality VR particle effects, I couldn't use the very typical method of making the particles billboards to look "good enough" and save processing power because people could see that they were looking at billboards, especially close up.
Probably the most important issue is performance. You now have a high resolution screen that needs to refresh at 90 frames a second or faster or someone's going to throw up. Video games in the past got used to thinking lower frame rates-- even as low as 30 FPS-- were perfectly acceptable, and if it stuttered a bit lower than that sometimes that was even fine.
The fact that performance requirements and expected quality levels are so steep now is forcing a lot of innovation in engine development. I personally love research into things like foveated rendering, light fields, and raytracing.
There's also a matter of ecosystem. You have to think about what hardware you're going to support. APIs (check out the new Khronos' VR working group) You have to think about mobile vs desktop platforms, and the performance differences there. You have to think about different controllers and headset and API quirks.
And more! If you're using an engine you won't need to worry about a lot of lower-level details. You'll need to keep performance in mind, think about what platforms you'll support, pick an engine to use or think about whether it's worth it to modify one, and also keep in mind what effects are better suited for VR when you create graphics in your game
Check out some of the resources above and feel free to ask follow up questions!