After leaving Buffy the Vampire Slayer, Angel went on to have five full seasons of his own self-titled series and several tie-in comic series both having to do with and without Buffy. He blazed his own trail in that specific part of the Whedonverse.
Angel and the comics have shown time and again that Angel was capable of all the action, drama, and comedy that were hallmarks of the series he came from. Since leaving Buffy, Angel amounted to a lot of developments that the flagship's fans might not be aware of.
10 Moves to Los Angeles and Opens Angel Investigations
Trading the small-town living for the big-city life, Angel makes his way to the City of Angels. There he eventually manages to settle down and open up his own detective agency. He then fills it up with friends new and old that would rival Buffy's own Scooby Gang including Cordelia, Doyle, Wesley, Gunn, Fred, Lorne, Fred, and more to take on the supernatural forces in Los Angeles.
Among all of the supernatural villains in LA that Angel met, the worst is Wolfram and Hart. A group of interdimensional lawyers that encompassed all of the bad stereotypes of the profession to the extreme. Led by a group of demons known as the Senior Partners, they spread evil throughout the series and beyond through their various "employees" like Holland Manners, Lilah Morgan, Marcus Hamilton, and Lindsey McDonald. Almost all of which were human, in a surprising change for the Buffyverse.
9 Had A Son
At the end of the first season, Wolfram and Hart resurrected Angel's ex and sire, Darla, and long story short, they would have a child. But only after Angel overthrows a shadow government and frees the human slaves in Lorne's home dimension of Pylea. Connor would then come into the world but only after Darla willingly sacrificed herself.
This would lead to a series of events where Connor would be kidnapped by Holtz (a former vampire hunter who hates Angel), whisked away to an alternate dimension, and then return as a teenager near the end of the same season due to the accelerated time flow in the dimension where he was raised. He would then come back and try to kill Angel because Holtz raised him to believe Angel was still Angelus. Ultimately, Connor would win a fight against his father. Then go on to have a child with Cordelia.
8 Angel Becomes Angelus Again
After surviving being imprisoned in a coffin at the bottom of the ocean by his son Connor, Angel would then lose his soul after a ritual forces him to experience a moment of happiness and turn him into Angelus.
Eventually, the group figures out that Angelus' connection with The Beast as well as most of the things that have transpired since Angel came to Los Angeles was all a ploy to get Jasmine, a rogue member of The Powers That Be, into the world through Cordelia and Connor's child. Jasmine wants nothing more but to bring world peace... at the cost of complete emotional enslavement of all humans. After briefly falling under Jasmine's spell, Angel eventually reveals her true name and shows everyone her real form. A fight between them then ensues; she threatens to wipe-out mankind and is eventually punched through the head by Connor. Cordelia falls into a coma during the events.
7 Becomes Part Of Wolfram And Hart
As thanks for stopping world peace, Wolfram and Hart offered Angel and company the job of being in charge of their Los Angeles branch. Seeing it as a good opportunity to obtain all of their information and steer the company into being a force for good, they all took it. Later it is also revealed that Angel agreed to the task because Wolfram and Hart agreed to erase Connors's memories from Connor and Angel's companions so that he could live a normal life. Adding another secret to Angel's wide list.
6 Spike Haunts Him
After his sacrifice at the end of Buffy, Spike reemerges as nothing more than a soul without a body from a mysterious amulet sent to them. He then proceeds to haunt Angel, half to annoy him and half because he has nothing better to do. Eventually, he gains corporeal form after another mysterious package returns him to normal. It then turns out that his revival was all orchestrated by Lindsey in an attempt to get revenge on Angel and Wolfram and Hart.
5 Kills Off The Circle Of The Black Thorn
Coming back monetarily to help Angel with Lindsey, Cordelia leaves Angel a parting gift of a vision before passing. In it, he finds out that the Circle of the Black Thorn, a group of powerful economical, political, and supernatural beings, are actually the people behind the apocalypse and vital to the Senior Partners of Wolfram and Hart.
He then attempts to join their ranks by acting uncharacteristically evil and even signs away his part of that Shanshu Prophecy that would have him earn his humanity after having a part in the apocalypse. Once he was in their good graces, he and the rest of Angel Investigations systematically killed each member. In return, the Senior Partners sent an army of supernatural creatures to deal with the surviving members of Angel's crew.
4 Goes To Hell, Literally
The comics were unique. The series starts exactly where the show ended. Fighting against a horde of demons, Angel manages a win the battle but not the war. Namely, the Senior Partners send Los Angeles straight to a Hell dimension. Worse yet, they turn Angel into a human right when he needed his supernatural powers the most. Though despite the setback, Angel continues to save the innocent, later defeats the Demon Lords that took up residence in Los Angeles, and then gets his head cut off by a vampiric Gunn.
3 Resets the Timeline
Thankfully, getting his head cut off was all part of the plan. While they may have enjoyed messing with Angel, they still needed him for their plans. So The Senior Partners were forced to reset the timeline to the point before Los Angeles fell. Reversing almost everything that has happened since, but with everyone's memory intact. Thus turning Angel and his friends into heroes around Los Angeles and revealing the supernatural to the world.
2 Kills And Resurrects Giles
After his time in the limelight, Angel becomes Twilight. His supervillain persona and the main antagonist to Buffy during season eight of the comics. He means well, and only became her enemy to stop a prophecy that would result in their deaths and the world falling into a Hell Dimension as Los Angeles did, but things turn out worse than for the better. By the end of the arc, Angel is possessed by Twilight (not his supervillain persona but the manifestation of an alternate reality he named himself after) and kills Giles. This then starts a long arc in the comics with Faith where Angel eventually resurrects Giles as a 12-year-old boy.
1 Magic Town and Archaeus
Magic town was the result of a borough in London that was created as a sanctuary for humans that were turned into demons by a magical plague ball created by Whistler, Nash, and Pearl in their attempt to "save the world" after Twilight's (the dimension, not Angel's) failure to do so. Archaeus is the progenitor of The Master's bloodline of vampires that included Spike, Drusilla, and Angel. Eventually, he would pit himself against Buffy when he tried to open a gate to Hell in San Francisco. Though, with the help of Angel, Buffy would destroy the artifact that would connect the two dimensions. Archaeus would later attempt to take over Magic Town by winning the members of the town over but failed to do so when they allied with Angel instead.