In October 2018, the Axie core team released the first battle system built on top of the Axie game assets. The battle system was structured as an "idle battle" system with inspiration from games like "Final Fantasy Tactics" and "Idle Heroes".
The Axie team started development on the real-time card battle system and application in March 2019 and released an Alpha in December 2019. As of October 2020, the Application has amassed over 15,000 downloads with over 7,000 weekly active users.
Much like Pokemon has gone through numerous iterations and types of battle systems, we also expect Axie to have many variations of battles over the years to come.
For an overview of the current battle system please see this guide.