My everyday phone for the past few years has been Nexus 4. I also have a Nexus 5, which is slightly larger and with a much better screen, but I never felt a need to switch (I did try to have "Let's use N5 this week" every once in a while, though). Last year's Nexus 6 simply felt too large for me. Besides, it is too expensive for me to buy.
I noticed that my N4 recently stopped picking up NFC and charging via wireless. Later I learned that this is a typical sign that its battery needs replacement. Not because the battery got too weak to hold charge, but because the battery started bloating, pushing against the back cover, which necessary antennas are built onto. By slightly raising the back cover by bulging out, the bloated battery breaks the connection from the motherboard to these antennas, which is made only by contact. And that is how NFC and wireless charging are broken.
At least, that is the story I read.
After learning how to, and getting a replacement battery and a few small screw/torx drivers, I opened the phone (which took me some time) and saw this bloated battery.
No wonder the back cover looked warped. After placing the new battery and closing the back, NFC started picking up very reliably and it charges properly on a wireless charger.