I'm running Ubuntu 16.04 and on my last few boots I have recieved a Low Disk Space message.
I brought up my system monitor and saw that my /boot directory /dev/sda1 was full. 
Clicking into the drive revealed a list of unused kernels.1 That is about 400MB worth of unused kernels on a 500MB boot partition.
There is plenty of advise on how to clean this up. The option that seemed safest to me is as follows.2
sudo apt autoremove --purge
You'll be asked of you are sure you want to continue. I choose yes, please be sure you understand what you are purging.
It took about five minutes to purge all of the unused kernels (this will vary depending upon how cluttered you partition is). You should see console output similar to the following.
Returning to your system monitor you'll notice your boot partition now has plenty of space.
