Destiny Emblem Collector is the most complete source for Destiny emblems: what they look like, exactly how to get them, and whether they're still available.
DEC currently tracks 1014 Destiny 2 emblems and 271 Destiny 1 emblems.
There are a few different places to get updates/patch notes from DEC and emblem news. All of these different places should have the same info posted to them, so follow wherever you spend your time!
Marathon Emblem Collector is currently in alpha! Come over and help test, see all the cool emblems, and help gather info!
There's a lot of stuff still under development (and Marathon doesn't have an API), so please pardon our dust! If you can help out in any way that would be great!