Riddler's Riddles solution and Riddler Trophies are collectibles in the game. There are a total of 21 of Riddler's Riddles to solve and 40 Riddler Trophies to collect. In the map menu, you can always check the progress of collectibles for each of the districts.

◈ Riddler Trophies are marked on the map if the player gets close to the location. By completing Riddler AR Challenges, solving Riddler's Riddles and completing side quests you will most likely find all 40 Riddler Trophies. You can always shoot to Riddler Trophies to drop it to the ground. For collecting all Riddler Trophies you will receive the following achievements:
⠀⠀◇ Stop Me If You've Heard This One - Collect 10 Riddler Trophies;
⠀⠀◇ The Oldest One in the Book! - Collect 40 Riddler Trophies.

◈ Riddler's Riddles solution is to find the right spot in the district and scan it with a scanner. There are three of them in each district. You can scan a building/sign from any perspective, not just the one in the guide. For solving all Riddler's Riddles you will receive the following achievements:
⠀⠀◇ The Right Question - Solve 5 of Riddler's Riddles;
⠀⠀◇ The Real Deal - Solve 21 of Riddler's Riddles.