I've been noticing somewhat granular "eras" of memes, from about 2000 to present. In the USA, at least.
Early 2000s: Newgrounds, birth of YouTube
From what I can tell, this time was dominated mainly by memes like advice animals (Philosoraptor, Scumbag Steve, etc), Flash animations (Peanut Butter Jelly banana, Badger Badger), and shorter viral YouTube videos (Charlie Bit My Finger, "Teleport Mario!", Angry German Kid, Leeroy Jenkins, etc).
This is what most people today would consider "classic memes."
Mid-2000s -- Early 2010s: YouTube Poops, Pepe, Rage Comics
It seems like soon after Youtube began (about 2-3 years), people started to make YTPs out of a whole bunch of stuff, like Downfall parodies, Nintendo CD-i cutscene edits, and more.
Pepe appears around 2005, and only grows in popularity from there. Rage comics also appear in this era, but become quickly discredited by the mid-2010s.
The memes here are considered old, but you can still see these hanging around (especially Pepe).
Early 2010s -- Mid 2010s: Irony
Now we have the ironic memes. After years of sincere memes, ironic memes seem to take it 180 degrees. MLG Parodies, dank memes, REEEE, replacement remixes, and more.
This era continues to be seen in present day,
Seems like we have a timeline of ironic memes, with comments offering other timelines
Mid-2010s -- Present: Surrealism, Fake News
Twitter stuff, Trump, fake news, and strange memes that make no sense. We're in this era right now.