While most hardware that you find in everyday use is already supported by the later Linux kernels (even by those you find in Debian stable), printers and scanners can be particularly tricky. These usually require specific drivers, which can vary not only from vendor to vendor, but there is no guarantee that two different models of the same vendor will work equally well.
The Linux Foundation’s Open Printing Database is an excellent source of information, whether you are looking to verify your existing printer’s compatibility, or planning to buy a new one and wondering whether it would work as expected.
For scanners, the Sane Project provides an excellent searchable database.
The full address of the Linux Foundation's printer database is https://wiki.linuxfoundation.org/en/OpenPrinting/Database/DatabaseIntro.
The full address of the Sane Projects searchable scanner database is http://www.sane-project.org/cgi-bin/driver.pl.