Regardless, they make an excellent couple. Jake and Amy don't go through the breakup and re-union routine. However, throughout the years, there have been several disclosures regarding them. Here are some details about their relationship from X-Men history.
Amy Adams (formerly Reisz) is a French mutant with the ability to control moisture in her environment. She first appeared in The Amazing Spider-Man #129 (May 1972). Her character was created by Stan Lee and Jack Kirby.
As with many Marvel characters at the time, Amy's origin was revised over time; she originally appeared as a brainwashed victim of the Red Skull who had been given powers by him. This version of the character first appeared in Captain America #250 (March 1974).
It is this original version of the character that is used in all subsequent appearances. She is one of the few characters that has never been revived or replaced after being killed off (although her daughter Jean recently made an appearance in All-New X-Men).
Amy married Peter Parker (the original Spider-Man) in an issue of Spectacular Spider-Man. They were divorced after just three issues because Peter wanted to focus on his career instead of marriage.
Previously, whenever she tried it, it never worked out. Jake and his followers across the world were devastated. Fortunately, Amy chooses to deviate from her rule for Jake. She sees her error and knows they're soul mates. So she breaks up with him by email.
She sends him a message saying that even though they've been through so much together, it's finally time for them to move on with their lives. She tells him that he's been in her mind every day since they met and that she loves him like he loves her. She concludes the email by telling him not to waste any more time because they're meant to be together forever.
After receiving the email, Jake goes into shock and collapses. When he wakes up, he doesn't remember anything about the accident. He assumes she saved him as usual and starts planning their wedding. However, when she doesn't reply to his messages, he comes to believe that she didn't mean what she said in the email and breaks down crying.
Meanwhile, back at the hospital, BMO realizes something is wrong when nobody comes to visit Jake. So he goes to check on him and finds him crying in pain. Realizing what has happened, BMO calls an ambulance and makes sure that Jake gets treated immediately. As soon as he recovers, Jake goes home to find Amy waiting for him.
Jake and Amy's stakeout connection never develops. Amy later begins dating Teddy. Which no one on the squad, notably Jake, enjoys. Jake is smitten with his new girlfriend, but Amy is growing dissatisfied with Teddy. They were sent on a work trip, and Jake invited Teddy and his new girlfriend. When they return, Teddy has been promoted and they aren't living up to their marriage contract so he leaves her alone.