What is lossless zoom and how does it work in the Lumia 1020 and Xperia Z1?

Smartphone cameras have been improving at a rapid pace, and while the field owes credit to many, it is Nokia, and as of late -- Sony -- that are at the helm. Every year, we're treated to larger sensors, more and bigger pixels, larger apertures, OIS, and more features than we can count. But one thing has been missing for a long while now, and that's proper zoom. After all, many a situation necessitate that you either get closer, or miss the shot, and in those cases you're pretty much done for if you have to rely on the traditional digital zoom. Sure, the objects do appear closer, but the price is often a prohibitive loss of detail, as the images are upscaled to the desired resolution with no regard to the actual resolution -- the image is stretched by the software, which then attempts to fill in the blanks as best as it can. Well, thanks to the giant sensors on the Nokia Lumia 1020 and Sony Xperia Z1/Z1 Compact, zoom is no longer a problem. But instead of opting for bulky zoom lens (Galaxy S4 Zoom), they both rely on their massive resolution in order to get what we call 'lossless' zoom.