Neal Adams and Dennis O'Neil were the co-creators of this team.
Oliver Queen/Hal Jordan:
The original team started when Green Lantern(Hal Jordan) and Green Arrow traveled across America to find their place in society after a suggestion by the latter member of the team. They dealt with supervillains, abductions as well as more realistic issues like drug use, brainwashing, pollution, etc.
During that time, the two was also meet various people including Black Canary, Green Arrow's love interest, Ali Appa Apsa, a Guardian, and Roy Harper, Oliver's sidekick. Although they had different political views, they had a tight-knit relationship with each other to the point that other heroes often comment on it.
After a few months, the two split and they grew apart for a while, particularly after Green Arrow kills someone and only meeting up once in Green Lantern #47 before the events of "Emerald Twilight" which the aftermath put a permanent stain, particularly Green Arrow's trust in Hal Jordan which lasted until before his temporary "death".
Connor Hawke/Kyle Rayner:
Connor Hawke and Kyle Rayner was the second Green Lantern/ Green Arrow duo who got together due to their similar circumstances as they try to pick up their respective heroes' legacies. Kyle, who's dealing as the only Green Lantern in the entire DC universe and to step out of Hal's former shadow while Connor after learning that Oliver Queen knows that he's his son and not getting to know him as well as using a different approach. The two also got to be friends.
The Resurrection of Green Arrow:
Green Arrow: Quiver brought back the original Green Arrow/Green Lantern relationship with a Oliver Queen who had memories of just ending his trip across America and it trying to workout what happened as he's in the modern world. It also had him meet Hal Jordan as the current Spectre at the time and changing his hood to his traditional Green Lantern uniform. Not long afterwords, Green Lantern: Rebirth had Hal Jordan returned to the living and with Oliver close to him.
Not long afterwards, they started to pair up in Green Lantern again and have been doing it until the end of the Justice League: Cry For Justice which broke their relationship again until they met up once in Brightest Day, the last partnership pre-Flashpoint and New 52.
Connor Hawke/ Hal Jordan:
From the minor story arc "Greener Pastures" and tangential to the famous Green Lantern story arc "Emerald Knights". Connor had met a younger version of Hal Jordan from his early days and paired up with him to learn a bit more about his and his father's past and is caught up in a repeat of a scenario that led to his father's death but with his skills and Hal's assistance, he stops it from repeating.
Oliver Queen/ Kyle Rayner:
In the story arc, "Black Circle: Urban Knights, the two work together to get to the bottom of a conspiracy involving an alien drug trade of bleach to fighting a massive intergalactic drug ring with arguments plenty as they struggle with two similar personalities but from different generations.