Hi Rachael, There were three layers of linoleum and we found out that the bottom layer was glued down with pine tar (?!) it came up with soap, water, and a big bristle broom/brush.
There were areas that had a little bit of linoleum glue and we just sanded them up with a hand orbital sander.

Thanks!!! I love Houzz and always look forward to the two weekly e-mails.
Rachael

We've had this problem too. I laid wet towels on it over night and in the morning it practically fell off with a little scrape from a putty knife. I was in shock, having spent years trying to get it up whole it was dry and tarry (this was in a laundry room).