In Pokémon X and Y, players can engage in various post-game activities and storylines that enhance the gameplay experience following their victory as Champion. Here’s a detailed overview of the key elements:

1. AZ Battle: One of the notable post-game activities is a battle against AZ, an important and enigmatic character from the game’s lore. After your Hall of Fame entry, players face AZ, who challenges you with a formidable team of level 60 Pokémon. This battle serves not only as a test of your skills but also reinforces the narrative elements surrounding AZ’s character and the history of the Kalos region.

2. Looker Sidequest: Following the completion of the main storyline, players can embark on a detective-style quest involving Looker, a recurring character in the Pokémon series. This sidequest begins after the player upgrades their Mega Ring and finishes a battle at the Battle Maison in Kiloude City. During this investigation, players interact with Professor Sycamore and uncover various mysteries, adding depth to the post-game experience.

3. Kiloude City Access: After becoming Champion, players gain access to Kiloude City, which serves as a hub for various post-game activities. In Kiloude City, you can find valuable items, engage in battles at the Battle Maison—a facility designed for competitive battles—and unlock opportunities to capture legendary Pokémon like Mewtwo and Zygarde. This area expands your gameplay options significantly.

4. National Pokédex: Upon reaching the post-game content, players receive the National Pokédex, which allows for the registration and capturing of Pokémon from other regions beyond Kalos. This addition encourages players to explore and complete their Pokédex, increasing the overall longevity of the game.

5. Competitive Battles and Rare Pokémon: The post-game also offers numerous opportunities for engaging in competitive battles, whether against other players or challenging NPC trainers. Additionally, players can hunt for rare Pokémon, including shinies, further enhancing the excitement and challenge of the game.

Overall, while the post-game content in Pokémon X and Y includes various sidequests, legendary Pokémon captures, and competitive facilities, it is crucial to note that it does not present a substantial narrative-driven story like earlier titles such as Pokémon Black 2 and White 2. Instead, it focuses more on exploration, character interactions, and battles rather than an expansive story arc.

In summary, Pokémon X and Y’s post-game experience is characterized by several engaging activities and challenges, but it lacks the deep and extensive narrative that some earlier Pokémon titles provided. Players are encouraged to explore new areas, participate in sidequests, and pursue legendary Pokémon, making for a fulfilling though concise post-game experience.