How to upgrade the kernel on the Raspberry pi

[Silla]

Hello,
I've noticed that "apt update" and "apt upgrade" never update the kernel on the raspberry pi. I guess this is by design, am I correct? I've tried installing the linux-image-armmp and I get a nice new kernel, but the raspberry always boots with the old kernel (by the way, I have to manually mount /boot before installing this package, otherwise apt happily copies the new kernel into /boot the mountpoint, instead of /boot the FAT partition). I've tried renaming the new kernel file into kernel7.img (I have a rpi 3), but all I get is an unbootable pi.
Are there some docs on how to upgrade the kernel on kali for the raspberry pi? I've done quite a bit of googling but couldn't find anything.

Thanks,
Silla