Path of the Past missions can be received from Chronomagi Taskers. Each quest has the reward of +1,000 faction with The Chronomancers, and the ability to buy a replica of the mission's target mob from Timeless Traders. When you reach sufficient faction you may also buy armor.
These missions count towards the Misson Achievements under your Quests Achievements tab.
You can only do one mission a day, with the timer running from 00:01 AM to 11:59 PM PST (Pacific Standard Time).