Originally Posted by
OOTCS
I think Natasha's history with the Avengers goes like this, based both on what I've read and what I've seen on the Fandom wiki:
After her initial relationship with Hawkeye, her handlers brainwashed her, she fought the Avengers, then she broke through the brainwashing and decided to become a civilian and Hawkeye's girlfriend. He wanted her to become an Avenger, but she was kind of meh on it, and then she was temporarily involved with SHIELD, and then she wanted to be a civilian again, and then she decided she wanted to strike off on her own. (Avengers #29-64)
Soon afterwards, Enchantress posing as Valkyrie put together a team of women called the Lady Liberators, supposedly as an anti-sexist version of the Avengers, and Natasha is one of the women included. "Valkyrie" persuaded her to join by reminding her about how the Avengers wouldn't let her join, but it's a bit of a stretch, because I think the Avengers would have let her join if she really wanted to, but she wasn't really into it at the time. (Avengers #76)
Then Natasha settles into her own identity as a superhero, dates Daredevil, and builds a new life in San Francisco. After the Scarlet Witch rejects him as a romantic interest, Hawkeye quits the Avengers and goes to confront Natasha over her breaking up with him. While he's there, the Avengers also approach Black Widow and Daredevil and ask them to join the team. They join for a single adventure and Daredevil turns down the invitation, but Black Widow decides to stay. This is her first stint as an Avenger, but she leaves after a single issue because she decides she wants to make things work with Matt. (Avengers #111-112)
Eventually, Natasha and Daredevil break up, and she joins the Champions. As a Champion, I think she teams up with the Avengers a few times (Avengers #151, 163, 173-177)
Over the years, Natasha shows up a couple of times when the Avengers are reorganizing their roster, but she doesn't actually join the team. (Avengers #181, 211, 221) In the last example of this, she thinks something along the lines of, "I should really get coffee with Hawkeye sometime!" And he thinks, "Every time I see her, my old feelings resurface!" But they don't actually interact or get that coffee.
In Avengers #239, the active roster is away in a mission but Wonder Man snagged a Letterman interview for the Avengers, so they call up a bunch of former members, including Natasha, to go on the show. This issue is also Hawkeye and Mockingbird's debut as a couple after having gotten married in the Hawkeye miniseries.
Natasha teams up with the Avengers again (East and West Coast branches this time!) in West Coast Avengers Annual #1, to help the teams figure out which former Avenger has been spreading lies about them to the US government. (Spoilers: It's Quicksilver. He's mad at the Avengers because Crystal cheated on him with Wanda and Vision's realtor.)
Black Widow finally joins the lineup for an extended time starting in Avengers #329, and she sticks with the team and even ends up leading the team until the Onslaught Saga that ends the book with issue #402. She's not "killed" with the rest of the Avengers, which gives her heavy survivor's guilt.
When the Avengers come back, she declines membership, but teams up with them and the Thunderbolts at least once during a crossover arc. This is circa-2000.
Later, after Disassembled, House of M, and Civil War, in 2007, she joins the pro-registration Avengers (which I still maintain was out of character for her, but to be fair, it was also out of character for most of the other pro-reg heroes) called the Mighty Avengers. This team disbands after Secret Invasion.
During the Heroic Age, she's part of Steve Rogers's Secret Avengers, which is not officially an Avengers team so much as a Black Ops team with a bunch of Avengers on the roster.
Then, in the real world, the MCU Avengers movie comes out in 2012. There's a matching 616 series called Avengers Assmble, which includes her and the other MCU "O6", and a year later, she's part of the cast of Hickman's Avengers. From that point on, Natasha has been on the Avengers quite a lot and is now considered by most to be an iconic Avenger rather than a street-level hero.