This page in our Borderlands 3 guide contains information on how to get eridium and what you can get with it. As a reminder, eridium is the premium currency in the game, and it is much harder to get than credits.
How to get eridium?
Eridium is received as a reward for completing Crew Challenges. These are challenges available on each of the maps. The challenges may require you to, for example, find dead Claptraps, steal unique vehicles, or collect audio logs.
Another method to get eridium are global challenges related to Guardian Ranks. You can check these challenges in the Galaxy View. They have many categories associated, for example, with eliminating enemies in certain ways, getting richer or using weapons from various manufacturers. You get eridium every time you reach a higher rank in a challenge.
Eridium can also appear as loot - you can, for example, get it by completing missions or by searching the bodies of defeated bosses or Loot Tinks.
Another form of loot are eridium deposits, or purple crystals, which you may encounter while exploring the game world. You can break them by using the melee attack button, but only after completing one of the storyline quests - Beneath the Eridian - this requirement is further described on a separate page (How to destroy purple crystals?) Destroying crystals leaves loot - eridium bars that can be picked up.
What can I get with eridium?
You can spend eridium on items offered by Crazy Earl on Sanctuary. The first option is to purchase cosmetics sold by Crazy Earl.
The second option is to visit Crazy Earl's vending machines that sell random powerful items. Just like with regular merchants, one of the offered items is categorized as "offer of the day" - this offer changes after some time.
You can also spend eridium on slot machines in the Sanctuary's canteen. You get a chance of winning a valuable reward.