Not to be confused with Challenge Missions.
Challenges are Competitive Missions against AI-controlled foes which aim to simulate and train PvP combat.
They are not Arenas, as no actual PvP combat takes place, although they make use of the same maps as those that are used in the PvP arena system.
Challenges have a distinct icon on the game map. At a glance it looks like a mission icon, but the "heraldic emblem" on the shield is different.
Currently there are only two challenges in the game:
More may be added later, or as part of Guild Wars Factions.