Not to be confused with the Wyvern Suppression Tank.
In a lot of fantasy settings, Wyverns are the less flashier versions of dragons.
Dungeons and Dragon
In Dungeons & Dragons a wyvern appears as a less powerful Dragon with two legs and wings and a stinging tail. They are typically a reddish brown, though other colors exist. While somewhat intelligent and capable of speech, they don't tend to use it, being ambush predators that are hostile by default to most things. Despite their aggression, they are often used as mounts in various settings.
In Eberron wyverns are found on both Argonnessen and Khorvaire. Various sources state they are used as mounts and that the Arcane Congress have breeding programs for them, and presumably House Vadalis does as well. They are featured in Breland's heraldry, but Thrane is the one stated to maintain wyvern units. Those of Argonnessen are subjugated by the true dragons of the land and serve as mounts for their human sized servants. Wild wyverns of Khorvaire are hostile to everything, even other wyverns outside of mating season. Presumably, like pigs, domesticated wyverns are less hostile to everything than their wild counterparts.
English translations of Fire Emblem has used the name "wyvern" to distinguish the domesticated dragon-like creatures that serve as mounts and can be mowed down by the dozens from the powerful and intelligent (true) dragons that are always of plot importance when they show up, despite the "wyverns" having front arms. The Japanese text instead calls the mounts the English word "dragon" and the plot important version "ryu". The 8th game includes a class with an actual wyvern mount, but it hasn't shown up again (and is a bit notorious for potentially crashing the game in the English version if you play with animations on).