Apple Upgrade Information can be found here.

According to Apple, the official compatible hardware list of Macs capable of running Mac OS High Sierra 10.13 is as follows:
High Sierra will run on 4 GB of RAM… 8 GB or more is better.

MacBook Pro (2010 and later)
MacBook Air (2010 and later)
Mac Mini (2010 and later)
Mac Pro (2010 and later)
MacBook (Late 2009 and later)
iMac (Late 2009 and later)

Only the following Macs support Mojave:

iMac models from 2012 or later
iMac Pro (from 2017)
MacBook models from 2015 or later
MacBook Pro models from 2012 or later
MacBook Air models from 2012 or later
Mac mini models from 2012 or later
Mac Pro models from late 2013 (plus mid-2010 and mid-2012 models with recommended Metal-capable GPU)

And for the geeky… a few others…

Before upgrading, check to see if your apps will be compatible in a newer operating system
Here's a
good site for checking upgradability.