There's not really that much to miss in regards to the whole Jasmine story-line.
Basically, W&H brought Darla back to sleep with Angel and turn him evil. He ****ed her, but she's just a slut, so he didn't go all evil. But like a season later she turned up pregnant with Angel's kid (no-one knows how). Enter Holtz. Nathaniel Holtz was some guy Angel ****ed with when he was evil, killed all his family and some such. So Holtz conspires with a time-travelling, non-corporeal demon called Sahjan who has found some prophecy saying Angel's kid will kill him (Sahjan).
So Holtz and Sahjan do all kinds of evil, nefarious things and it ends up with Holtz running off with Connor (Angel's kid) into a dimensional portal to the 'darkest of the dark worlds'. Wesley also gets his throat cut by one of Holtz's goons and almost dies.
Cordelia was being killed by the visions as they were never meant to be contained within a human, so she gets demon'd up some.
There's a bigass portal to the hell dimension Connor went to in the middle of the Hotel the good guys are working from and all these demon things keep popping out saying they're running from 'The Destroyer'. Turns out the Destroyer is Connor, who thanks to some temporal-screwage between the two dimensions, is now like 17 and has been trained by Holtz to be one kickass fighter. And he's out to kill Angel.
Lots of stuff happens, Connor goes evil and dumps Angel to the bottom of the ocean on the night that demon-Cordy ascends to fight the good fight on a higher plane of existence.
A while later, Cordy comes back with her memory lost and, unbeknownst to everyone, is evil as hell. She conjours up all kinds of badness and hires this invincible demon known as the Beast to block out the sun and give the vampires a free-for-all.
As fire rains down on LA (another evil-Cordy spell) she and Connor get freaky and he knocks her up. She later gives birth to a Power That Was called Jasmine who everyone loves (magic) and goes into a coma. Turns out all the evilness was just 'birthing pains'.
They then defeat Jasmine on the eve of her mind-****ing the whole world and making Earth into a paradise at the cost of everyone's free will. And Connor goes nuts.
His love (Cordy) is in a coma, Jasmine (his daughter who promised peace on Earth) is dead and he still hates Angel. So he grabs a bomb, heads to a church with coma-Cordy and tries to kill a few hundred people.
It's about this time that W&H pop up and say "We're sick of fighting you, Angel. You can run the LA W&H and try to reign in our evil deeds, and we'll make everyone forget Connor and give him a kickass life with a real family". Angel accepts and ends up the CEO of LA W&H.
An amulet gets delivered to W&H, the same one that Spike was wearing when he destroyed the Hellmouth in Buffy, and Spike pops out as a ghost. He's later made flesh by some magic.
Skip ahead about half a season and Fred gets virus'd by this sarcophagus containing the essence of one of the oldest of the old demons called Illyria (there's thousands of such sarcs in the Deeper Well, which is guarded by Drogyn). Fred is gone. Totally. Her soul was destroyed in the 'fires of ressurection'.
Gunn gets left in a holding dimension where his heart gets cut out once a day by a W&H demon because they get Lindsey out (he knows things about the Senior Partners) but someone needs to take his place.
Illyria then goes charging in and slaughters everyone with her God-like powes and gets Gunn out.
Hamilton, the Terminator-esque guy who is Angel's liason to the senior partners, hints that the Wolf, Ram and Hart and pissing in their panites about Illyria. Illyria says that when she ruled the world a few million years ago the Wolf, Ram and Hart were barely above the Vampire.
Illyria almost explodes because Fred's body can't hold her power and she ends up getting a load of her power drained off into a vacuum dimension, leaving her stronger than everyone else, but pretty powerless compared to her old self.
Then comes Cyvus Vale. He's the demon W&H used to change all the world's memories of Connor and he blackmails Angel into having Connor fight his old enemy Sahjan, who Angel trapped inside an ancient bottle thing after the senior partners made him corporeal.
Connor kicks Sahjan's ass and thanks to Wesley's tampering, gets his memories back in the process.
Through Vale, Angel hooks up with the Circle of the Black Thorn, the most powerful darkness in the whole world. It has members such as Vale and the powerful demon warlord Sebbassis. Angel kills Drogyn to prove to them that he's evil enough. He also signs away the possibility of ever becoming human again (the Shanshu Prophecy foretold it, but he signs the Prophecy to say he renounces the reward for his good deeds).
And that's where the finale picks up.
