In canon, Espio and Vector often appear together (usually along with Charmy Bee) as they are members of the Chaotix.
Vector and Espio both made their debut in Knuckles' Chaotix. As that game paired two characters out of the set of playable characters, there was a chance Espio and Vector could get paired. During that time, besides Espio and Vector, the Chaotix consisted of Knuckles, Charmy, and Mighty.
Later, in Sonic Heroes, the team had gone down in size to just the two and Charmy. Espio and Vector were relaxing in the office when Charmy came in, informing the two of a new job they got. Espio felt suspicious about the job, but Vector reminded him that the Chaotix never turned down work that paid. Espio followed Vector's orders and the three went to Seaside Hill to find hermit crabs. After fourteen missions and fights with a fake Eggman and other teams, the Chaotix found their client, the real Eggman. The Chaotix learned that Eggman was locked up by Metal Sonic, and later the Chaotix helped Team Sonic, Dark and Rose defeat Neo Metal Sonic.
In Shadow the Hedgehog, the Chaotix was working on a case involving Gerald Robotnik. Vector had given Espio the task to hack Dr. Eggman's computer. The hacking did not go well, and Vector kept rushing Espio while keeping Charmy silent. When Shadow arrived, Vector asked him for help. Shadow smashed the computer, opening a portal to Mad Matrix and entering. Vector told Espio to follow Shadow into the portal.
Later, the three were hacking the main computer on the Space Colony ARK. Again, Espio was given the task of hacking while Vector tried to keep Charmy from interfering. However, Charmy rammed the computer, resulting in them getting a video clip by Gerald Robotnik appear on various screens around the world and Black Comet.
In Sonic Rivals 2, Vector gave Espio the task to find evidence that Silver the Hedgehog was behind the Chao disappearences. However, shortly afterwards, the two had communication issues, and only got to talk to each other after Silver had already left. Vector asked if Silver was behind the Chao disappearences, which Espio confirmed, but got furious as Espio did not have any evidence.
Espio and Vector were among the guests that attended Sonic's birthday party in the console and PC versions of Sonic Generations. However, during the party, Espio, Vector and the rest of the guests were pulled into the white realm and frozen. Both were eventually rescued by Sonic and Classic Sonic. Espio and Vector showed up with the rest of Sonic's rescued friends, as well as Shadow and Silver, to cheer the Sonics on in their battle against the Time Eater. After the battle was over, Vector and Espio returned to the birthday party.
Espio and Vector have both appeared in every installment of the Mario & Sonic series, but while Vector was playable in all of them, Espio was only playable in Rio 2016. Both also appeared as Chaotix Type characters in Sonic Runners and Sonic Runners Adventure.
Espio and Vector keep their roles as Chaotix members in all major comic adaptions of the series, which are Sonic the Comic, both Pre- and Post-Super Genesis Wave Archie comics and the comics by IDW Publishing.
Like in the games, Vector and Espio are members of the Chaotix along with Charmy Bee. The three were transported to Earth along with their office.
Vecpio is among the most popular ships for both characters and the most popular slash ship for Vector. The pairing has notably more support than their respective ships with Charmy, most likely due to Charmy being notably younger than the two.
On AO3, it is the most popular ship for Espio and the second most popular ship for Vector, behind Vanilla/Vector.