A few days ago I bought my first Raspberry Pi, a Zero W. I installed Arch ARM on it, and configured wpa_supplicant during the installation (as per these instructions https://ladvien.com/installing-arch-linux-raspberry-pi-zero-w/). That went quite well, rp0w booted without problems, I could SSH in, I could ping internet by ip addresses, BUT.... I never could get the name resolution working with default settings & programs. To have a working name resolution, I had to 1) stop and disable both systemd-networkd and systemd-resolved, 2) start and enable dhcpcd on wlan0 and 3) edit /etc/resolv.conf by hand. (to stop dhcpcd overwriting it I added 'nohook resolv.conf' to /etc/dhcpcd.conf). I should also mention that none of the other computers in my network has any problems with DNS or routing, including the two other Arch Linux machines (those two are using NetworkManager, though)
Any ideas why systemd-resolved couldn't do its job? According to a quick search through these forums it seems like quite a few new users have the same problem...